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Deck 15: Multiple Regression Model Building
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TABLE 15-1
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = β₀ + β₁X + β₁X² + ε
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
Referring to Table 15-1, what is the correct interpretation of the coefficient of multiple determination?
A) 98.8% of the total variation in demand can be explained by the linear relationship between demand and price.
B) 98.8% of the total variation in demand can be explained by the quadratic relationship between demand and price.
C) 98.8% of the total variation in demand can be explained by the addition of the square term in price.
D) 98.8% of the total variation in demand can be explained by just the square term in price.
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = β₀ + β₁X + β₁X² + ε
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
Referring to Table 15-1, what is the correct interpretation of the coefficient of multiple determination?
A) 98.8% of the total variation in demand can be explained by the linear relationship between demand and price.
B) 98.8% of the total variation in demand can be explained by the quadratic relationship between demand and price.
C) 98.8% of the total variation in demand can be explained by the addition of the square term in price.
D) 98.8% of the total variation in demand can be explained by just the square term in price.
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TABLE 15-1
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = β₀ + β₁X + β₁X² + ε
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
Referring to Table 15-1, what is the p-value associated with the test statistic for testing whether there is an upward curvature in the response curve relating the demand (Y) and the price (X)?
A) 0.0001
B) 0.0006
C) 0.3647
D) None of the above.
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = β₀ + β₁X + β₁X² + ε
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
Referring to Table 15-1, what is the p-value associated with the test statistic for testing whether there is an upward curvature in the response curve relating the demand (Y) and the price (X)?
A) 0.0001
B) 0.0006
C) 0.3647
D) None of the above.
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TABLE 15-2
Referring to Table 15-2, is the overall model statistically adequate at a 0.05 level of significance for predicting sale price (Y)?
A) No, since some of the t tests for the individual variables are not significant.
B) No, since the standard deviation of the model is fairly large.
C) Yes, since none of the β-estimates are equal to 0.
D) Yes, since the p-value for the test is smaller than 0.05.
Referring to Table 15-2, is the overall model statistically adequate at a 0.05 level of significance for predicting sale price (Y)?
A) No, since some of the t tests for the individual variables are not significant.
B) No, since the standard deviation of the model is fairly large.
C) Yes, since none of the β-estimates are equal to 0.
D) Yes, since the p-value for the test is smaller than 0.05.
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TABLE 15-1
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = β₀ + β₁X + β₁X² + ε
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
Referring to Table 15-1, what is the value of the test statistic for testing whether there is an upward curvature in the response curve relating the demand (Y) and the price (X)?
A) -5.14
B) 0.95
C) 373
D) None of the above.
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = β₀ + β₁X + β₁X² + ε
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
Referring to Table 15-1, what is the value of the test statistic for testing whether there is an upward curvature in the response curve relating the demand (Y) and the price (X)?
A) -5.14
B) 0.95
C) 373
D) None of the above.
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TABLE 15-1
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = β₀ + β₁X + β₁X² + ε
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
Referring to Table 15-1, a more parsimonious simple linear model is likely to be statistically superior to the fitted curvilinear for predicting sale price (Y).
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = β₀ + β₁X + β₁X² + ε
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
Referring to Table 15-1, a more parsimonious simple linear model is likely to be statistically superior to the fitted curvilinear for predicting sale price (Y).
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TABLE 15-1
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = β₀ + β₁X + β₁X² + ε
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
Referring to Table 15-1, does there appear to be significant upward curvature in the response curve relating the demand (Y) and the price (X) at 10% level of significance?
A) Yes, since the p-value for the test is less than 0.10.
B) No, since the value of β is near 0.
C) No, since the p-value for the test is greater than 0.10.
D) Yes, since the value of β is positive.
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = β₀ + β₁X + β₁X² + ε
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
Referring to Table 15-1, does there appear to be significant upward curvature in the response curve relating the demand (Y) and the price (X) at 10% level of significance?
A) Yes, since the p-value for the test is less than 0.10.
B) No, since the value of β is near 0.
C) No, since the p-value for the test is greater than 0.10.
D) Yes, since the value of β is positive.
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TABLE 15-2
Referring to Table 15-2, given a quadratic relationship between sale price (Y) and property size (X₁), what test should be used to test whether the curves differ from cove and non-cove properties?
A) F test for the entire regression model
B) t test on each of the coefficients in the entire regression model
C) Partial F test on the subset of the appropriate coefficients
D) t test on each of the subsets of the appropriate coefficients
Referring to Table 15-2, given a quadratic relationship between sale price (Y) and property size (X₁), what test should be used to test whether the curves differ from cove and non-cove properties?
A) F test for the entire regression model
B) t test on each of the coefficients in the entire regression model
C) Partial F test on the subset of the appropriate coefficients
D) t test on each of the subsets of the appropriate coefficients
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TABLE 15-2
Referring to Table 15-2, given a quadratic relationship between sale price (Y) and property size (X₁), what null hypothesis would you test to determine whether the curves differ from cove and non-cove properties?
A) H₀: β₂ = β₃ = β₅ = 0
B) H₀: β₄ = β₅ = 0
C) H₀: β₃ = β₅ = 0
D) H₀: β₂ = 0
Referring to Table 15-2, given a quadratic relationship between sale price (Y) and property size (X₁), what null hypothesis would you test to determine whether the curves differ from cove and non-cove properties?
A) H₀: β₂ = β₃ = β₅ = 0
B) H₀: β₄ = β₅ = 0
C) H₀: β₃ = β₅ = 0
D) H₀: β₂ = 0
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TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose. If she chooses to use a level of significance of 0.01 she would decide that there is a significant curvilinear relationship.
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose. If she chooses to use a level of significance of 0.01 she would decide that there is a significant curvilinear relationship.
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TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a curvilinear model that includes a linear term. The p-value of the test statistic for the contribution of the curvilinear term is ________.
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a curvilinear model that includes a linear term. The p-value of the test statistic for the contribution of the curvilinear term is ________.
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TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose. The p-value of the test is ________.
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose. The p-value of the test is ________.
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TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a curvilinear model that includes a linear term. If she used a level of significance of 0.05, she would decide that the linear model is sufficient.
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a curvilinear model that includes a linear term. If she used a level of significance of 0.05, she would decide that the linear model is sufficient.
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TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose. If she chooses to use a level of significance of 0.05, she would decide that there is a significant curvilinear relationship.
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose. If she chooses to use a level of significance of 0.05, she would decide that there is a significant curvilinear relationship.
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TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a curvilinear model that includes a linear term. If she used a level of significance of 0.01, she would decide that the linear model is sufficient.
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a curvilinear model that includes a linear term. If she used a level of significance of 0.01, she would decide that the linear model is sufficient.
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TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose. The value of the test statistic is ________.
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose. The value of the test statistic is ________.
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TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, the prediction of time to relief for a person receiving a dose of the drug 10 units above the mean dose (i.e., the prediction of Y for X = 10) is ________.
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, the prediction of time to relief for a person receiving a dose of the drug 10 units above the mean dose (i.e., the prediction of Y for X = 10) is ________.
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TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if the linear term is significant. The p-value of the test is ________.
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if the linear term is significant. The p-value of the test is ________.
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TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if the linear term is significant. Using a level of significance of 0.05, she would decide that the linear term is significant.
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if the linear term is significant. Using a level of significance of 0.05, she would decide that the linear term is significant.
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TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if the linear term is significant. The value of the test statistic is ________.
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if the linear term is significant. The value of the test statistic is ________.
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TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, there is reason to suspect collinearity between some pairs of predictors.
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, there is reason to suspect collinearity between some pairs of predictors.
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TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the residual plot suggests that a nonlinear model on % attendance may be a better model.
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the residual plot suggests that a nonlinear model on % attendance may be a better model.
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TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the better model using a 5% level of significance derived from the "best" model above is
A) X₁.
B) X₃.
C) X₁,X₃.
D) X₁,X₂,X₃.
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the better model using a 5% level of significance derived from the "best" model above is
A) X₁.
B) X₃.
C) X₁,X₃.
D) X₁,X₂,X₃.
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TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, what are, respectively, the values of the variance inflationary factor of the 3 predictors?
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, what are, respectively, the values of the variance inflationary factor of the 3 predictors?
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TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, which of the following predictors should first be dropped to remove collinearity?
A) X₁
B) X₂
C) X₃
D) None of the above
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, which of the following predictors should first be dropped to remove collinearity?
A) X₁
B) X₂
C) X₃
D) None of the above
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TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, which of the following models should be taken into consideration using the Mallows' Cp statistic?
A) X₁,X₃
B) X₁,X₂,X₃
C) Both of the above
D) None of the above
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, which of the following models should be taken into consideration using the Mallows' Cp statistic?
A) X₁,X₃
B) X₁,X₂,X₃
C) Both of the above
D) None of the above
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TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the "best" model chosen using the adjusted R-square statistic is
A) X₁,X₃.
B) X₁,X₂,X₃.
C) Either of the above
D) None of the above
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the "best" model chosen using the adjusted R-square statistic is
A) X₁,X₃.
B) X₁,X₂,X₃.
C) Either of the above
D) None of the above
Question
Question
TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the "best" model using a 5% level of significance among those chosen by the Cp statistic is
A) X₁,X₃.
B) X₁,X₂,X₃.
C) Either of the above
D) None of the above
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the "best" model using a 5% level of significance among those chosen by the Cp statistic is
A) X₁,X₃.
B) X₁,X₂,X₃.
C) Either of the above
D) None of the above
Question
Question
Question
Question
TABLE 15-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Age?
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Age?
Question
TABLE 15-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Head?
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Head?
Question
TABLE 15-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, the variable X₃ should be dropped to remove collinearity.
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, the variable X₃ should be dropped to remove collinearity.
Question
TABLE 15-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, the variable X₂ should be dropped to remove collinearity.
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, the variable X₂ should be dropped to remove collinearity.
Question
Question
TABLE 15-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, there is reason to suspect collinearity between some pairs of predictors based on the values of the variance inflationary factor.
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, there is reason to suspect collinearity between some pairs of predictors based on the values of the variance inflationary factor.
Question
TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, what is the value of the test statistic to determine whether the quadratic effect of daily average of the percentage of students attending class on percentage of students passing the proficiency test is significant at a 5% level of significance?
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, what is the value of the test statistic to determine whether the quadratic effect of daily average of the percentage of students attending class on percentage of students passing the proficiency test is significant at a 5% level of significance?
Question
Question
TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the null hypothesis should be rejected when testing whether the quadratic effect of daily average of the percentage of students attending class on percentage of students passing the proficiency test is significant at a 5% level of significance.
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the null hypothesis should be rejected when testing whether the quadratic effect of daily average of the percentage of students attending class on percentage of students passing the proficiency test is significant at a 5% level of significance.
Question
TABLE 15-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Edu?
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Edu?
Question
Question
Question
Question
TABLE 15-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Job Yr?
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Job Yr?
Question
TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, what is the p-value of the test statistic to determine whether the quadratic effect of daily average of the percentage of students attending class on percentage of students passing the proficiency test is significant at a 5% level of significance?
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, what is the p-value of the test statistic to determine whether the quadratic effect of daily average of the percentage of students attending class on percentage of students passing the proficiency test is significant at a 5% level of significance?
Question
Question
TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the quadratic effect of daily average of the percentage of students attending class on percentage of students passing the proficiency test is not significant at a 5% level of significance.
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the quadratic effect of daily average of the percentage of students attending class on percentage of students passing the proficiency test is not significant at a 5% level of significance.
Question
TABLE 15-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Married?
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Married?
Question
TABLE 15-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Manager?
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Manager?
Question
TABLE 15-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, the variable X₁ should be dropped to remove collinearity.
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, the variable X₁ should be dropped to remove collinearity.
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Deck 15: Multiple Regression Model Building
1
The Variance Inflationary Factor (VIF) measures the correlation of the X variables with the Y variable.
False
2
TABLE 15-1
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = β₀ + β₁X + β₁X² + ε
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
Referring to Table 15-1, what is the correct interpretation of the coefficient of multiple determination?
A) 98.8% of the total variation in demand can be explained by the linear relationship between demand and price.
B) 98.8% of the total variation in demand can be explained by the quadratic relationship between demand and price.
C) 98.8% of the total variation in demand can be explained by the addition of the square term in price.
D) 98.8% of the total variation in demand can be explained by just the square term in price.
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = β₀ + β₁X + β₁X² + ε
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
Referring to Table 15-1, what is the correct interpretation of the coefficient of multiple determination?
A) 98.8% of the total variation in demand can be explained by the linear relationship between demand and price.
B) 98.8% of the total variation in demand can be explained by the quadratic relationship between demand and price.
C) 98.8% of the total variation in demand can be explained by the addition of the square term in price.
D) 98.8% of the total variation in demand can be explained by just the square term in price.
B
3
Collinearity is present when there is a high degree of correlation between the dependent variable and any of the independent variables.
False
4
A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. A statistical analyst discovers that capital spending by corporations has a significant inverse relationship with wage spending. What should the microeconomist who developed this multiple regression model be particularly concerned with?
A) Randomness of error terms
B) Collinearity
C) Normality of residuals
D) Missing observations
A) Randomness of error terms
B) Collinearity
C) Normality of residuals
D) Missing observations
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5
TABLE 15-1
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = β₀ + β₁X + β₁X² + ε
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
Referring to Table 15-1, what is the p-value associated with the test statistic for testing whether there is an upward curvature in the response curve relating the demand (Y) and the price (X)?
A) 0.0001
B) 0.0006
C) 0.3647
D) None of the above.
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = β₀ + β₁X + β₁X² + ε
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
Referring to Table 15-1, what is the p-value associated with the test statistic for testing whether there is an upward curvature in the response curve relating the demand (Y) and the price (X)?
A) 0.0001
B) 0.0006
C) 0.3647
D) None of the above.
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6
If independent variables are not significant individually but are significant as a group at a specified level of significance, this is most likely due to
A) autocorrelation.
B) the presence of dummy variables.
C) the absence of dummy variables.
D) collinearity.
A) autocorrelation.
B) the presence of dummy variables.
C) the absence of dummy variables.
D) collinearity.
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TABLE 15-2
Referring to Table 15-2, is the overall model statistically adequate at a 0.05 level of significance for predicting sale price (Y)?
A) No, since some of the t tests for the individual variables are not significant.
B) No, since the standard deviation of the model is fairly large.
C) Yes, since none of the β-estimates are equal to 0.
D) Yes, since the p-value for the test is smaller than 0.05.
Referring to Table 15-2, is the overall model statistically adequate at a 0.05 level of significance for predicting sale price (Y)?
A) No, since some of the t tests for the individual variables are not significant.
B) No, since the standard deviation of the model is fairly large.
C) Yes, since none of the β-estimates are equal to 0.
D) Yes, since the p-value for the test is smaller than 0.05.
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TABLE 15-1
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = β₀ + β₁X + β₁X² + ε
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
Referring to Table 15-1, what is the value of the test statistic for testing whether there is an upward curvature in the response curve relating the demand (Y) and the price (X)?
A) -5.14
B) 0.95
C) 373
D) None of the above.
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = β₀ + β₁X + β₁X² + ε
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
Referring to Table 15-1, what is the value of the test statistic for testing whether there is an upward curvature in the response curve relating the demand (Y) and the price (X)?
A) -5.14
B) 0.95
C) 373
D) None of the above.
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9
A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and constructed the multiple regression model. The business literature involving human capital shows that education influences an individual's annual income. Combined, these may influence family size. With this in mind, what should the real estate builder be particularly concerned with when analyzing the multiple regression model?
A) Randomness of error terms
B) Collinearity
C) Normality of residuals
D) Missing observations
A) Randomness of error terms
B) Collinearity
C) Normality of residuals
D) Missing observations
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10
The Cp statistic is used
A) to determine if there is a problem of collinearity.
B) if the variances of the error terms are all the same in a regression model.
C) to choose the best model.
D) to determine if there is an irregular component in a time series.
A) to determine if there is a problem of collinearity.
B) if the variances of the error terms are all the same in a regression model.
C) to choose the best model.
D) to determine if there is an irregular component in a time series.
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11
TABLE 15-1
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = β₀ + β₁X + β₁X² + ε
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
Referring to Table 15-1, a more parsimonious simple linear model is likely to be statistically superior to the fitted curvilinear for predicting sale price (Y).
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = β₀ + β₁X + β₁X² + ε
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
Referring to Table 15-1, a more parsimonious simple linear model is likely to be statistically superior to the fitted curvilinear for predicting sale price (Y).
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12
TABLE 15-1
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = β₀ + β₁X + β₁X² + ε
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
Referring to Table 15-1, does there appear to be significant upward curvature in the response curve relating the demand (Y) and the price (X) at 10% level of significance?
A) Yes, since the p-value for the test is less than 0.10.
B) No, since the value of β is near 0.
C) No, since the p-value for the test is greater than 0.10.
D) Yes, since the value of β is positive.
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
Y = β₀ + β₁X + β₁X² + ε
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
Referring to Table 15-1, does there appear to be significant upward curvature in the response curve relating the demand (Y) and the price (X) at 10% level of significance?
A) Yes, since the p-value for the test is less than 0.10.
B) No, since the value of β is near 0.
C) No, since the p-value for the test is greater than 0.10.
D) Yes, since the value of β is positive.
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13
Collinearity is present when there is a high degree of correlation between independent variables.
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14
The Variance Inflationary Factor (VIF) measures the
A) correlation of the X variables with the Y variable.
B) correlation of the X variables with each other.
C) contribution of each X variable with the Y variable after all other X variables are included in the model.
D) standard deviation of the slope.
A) correlation of the X variables with the Y variable.
B) correlation of the X variables with each other.
C) contribution of each X variable with the Y variable after all other X variables are included in the model.
D) standard deviation of the slope.
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15
A regression diagnostic tool used to study the possible effects of collinearity is
A) the slope.
B) the Y-intercept.
C) the VIF.
D) the standard error of the estimate.
A) the slope.
B) the Y-intercept.
C) the VIF.
D) the standard error of the estimate.
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16
In multiple regression, the ________ procedure permits variables to enter and leave the model at different stages of its development.
A) forward selection
B) residual analysis
C) backward elimination
D) stepwise regression
A) forward selection
B) residual analysis
C) backward elimination
D) stepwise regression
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17
Which of the following is used to find a "best" model?
A) Odds ratio
B) Mallow's Cp
C) Standard error of the estimate
D) SST
A) Odds ratio
B) Mallow's Cp
C) Standard error of the estimate
D) SST
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18
TABLE 15-2
Referring to Table 15-2, given a quadratic relationship between sale price (Y) and property size (X₁), what test should be used to test whether the curves differ from cove and non-cove properties?
A) F test for the entire regression model
B) t test on each of the coefficients in the entire regression model
C) Partial F test on the subset of the appropriate coefficients
D) t test on each of the subsets of the appropriate coefficients
Referring to Table 15-2, given a quadratic relationship between sale price (Y) and property size (X₁), what test should be used to test whether the curves differ from cove and non-cove properties?
A) F test for the entire regression model
B) t test on each of the coefficients in the entire regression model
C) Partial F test on the subset of the appropriate coefficients
D) t test on each of the subsets of the appropriate coefficients
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19
As a project for his business statistics class, a student examined the factors that determined parking meter rates throughout the campus area. Data were collected for the price per hour of parking, blocks to the quadrangle, and one of the three jurisdictions: on campus, in downtown and off campus, or outside of downtown and off campus. The population regression model hypothesized is Yᵢ = β₀ + β₁X₁ᵢ + β₂X₂ᵢ + β₃X₃ᵢ + ε where
Y is the meter price
X₁ is the number of blocks to the quad
X₂ is a dummy variable that takes the value 1 if the meter is located in downtown and off campus and the value 0 otherwise
X₃ is a dummy variable that takes the value 1 if the meter is located outside of downtown and off campus, and the value 0 otherwise
Suppose that whether the meter is located on campus is an important explanatory factor. Why should the variable that depicts this attribute not be included in the model?
A) Its inclusion will introduce autocorrelation.
B) Its inclusion will introduce collinearity.
C) Its inclusion will inflate the standard errors of the estimated coefficients.
D) Both B and C.
Y is the meter price
X₁ is the number of blocks to the quad
X₂ is a dummy variable that takes the value 1 if the meter is located in downtown and off campus and the value 0 otherwise
X₃ is a dummy variable that takes the value 1 if the meter is located outside of downtown and off campus, and the value 0 otherwise
Suppose that whether the meter is located on campus is an important explanatory factor. Why should the variable that depicts this attribute not be included in the model?
A) Its inclusion will introduce autocorrelation.
B) Its inclusion will introduce collinearity.
C) Its inclusion will inflate the standard errors of the estimated coefficients.
D) Both B and C.
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20
TABLE 15-2
Referring to Table 15-2, given a quadratic relationship between sale price (Y) and property size (X₁), what null hypothesis would you test to determine whether the curves differ from cove and non-cove properties?
A) H₀: β₂ = β₃ = β₅ = 0
B) H₀: β₄ = β₅ = 0
C) H₀: β₃ = β₅ = 0
D) H₀: β₂ = 0
Referring to Table 15-2, given a quadratic relationship between sale price (Y) and property size (X₁), what null hypothesis would you test to determine whether the curves differ from cove and non-cove properties?
A) H₀: β₂ = β₃ = β₅ = 0
B) H₀: β₄ = β₅ = 0
C) H₀: β₃ = β₅ = 0
D) H₀: β₂ = 0
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21
Collinearity is present if the dependent variable is linearly related to one of the explanatory variables.
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22
TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose. If she chooses to use a level of significance of 0.01 she would decide that there is a significant curvilinear relationship.
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose. If she chooses to use a level of significance of 0.01 she would decide that there is a significant curvilinear relationship.
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23
TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a curvilinear model that includes a linear term. The p-value of the test statistic for the contribution of the curvilinear term is ________.
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a curvilinear model that includes a linear term. The p-value of the test statistic for the contribution of the curvilinear term is ________.
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24
TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose. The p-value of the test is ________.
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose. The p-value of the test is ________.
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25
So that we can fit curves as well as lines by regression, we often use mathematical manipulations for converting one variable into a different form. These manipulations are called dummy variables.
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26
Two simple regression models were used to predict a single dependent variable. Both models were highly significant, but when the two independent variables were placed in the same multiple regression model for the dependent variable, R² did not increase substantially and the parameter estimates for the model were not significantly different from 0. This is probably an example of collinearity.
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27
TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a curvilinear model that includes a linear term. If she used a level of significance of 0.05, she would decide that the linear model is sufficient.
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a curvilinear model that includes a linear term. If she used a level of significance of 0.05, she would decide that the linear model is sufficient.
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28
TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose. If she chooses to use a level of significance of 0.05, she would decide that there is a significant curvilinear relationship.
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose. If she chooses to use a level of significance of 0.05, she would decide that there is a significant curvilinear relationship.
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29
A high value of R² significantly above 0 in multiple regression accompanied by insignificant t-values on all parameter estimates very often indicates a high correlation between independent variables in the model.
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30
In multiple regression, the ________ procedure permits variables to enter and leave the model at different stages of its development.
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31
One of the consequences of collinearity in multiple regression is inflated standard errors in some or all of the estimated slope coefficients.
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32
TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a curvilinear model that includes a linear term. If she used a level of significance of 0.01, she would decide that the linear model is sufficient.
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a curvilinear model that includes a linear term. If she used a level of significance of 0.01, she would decide that the linear model is sufficient.
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33
TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose. The value of the test statistic is ________.
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose. The value of the test statistic is ________.
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34
TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, the prediction of time to relief for a person receiving a dose of the drug 10 units above the mean dose (i.e., the prediction of Y for X = 10) is ________.
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, the prediction of time to relief for a person receiving a dose of the drug 10 units above the mean dose (i.e., the prediction of Y for X = 10) is ________.
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35
Collinearity will result in excessively low standard errors of the parameter estimates reported in the regression output.
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36
The parameter estimates are biased when collinearity is present in a multiple regression equation.
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37
TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if the linear term is significant. The p-value of the test is ________.
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if the linear term is significant. The p-value of the test is ________.
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38
TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if the linear term is significant. Using a level of significance of 0.05, she would decide that the linear term is significant.
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if the linear term is significant. Using a level of significance of 0.05, she would decide that the linear term is significant.
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39
TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if the linear term is significant. The value of the test statistic is ________.
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
Referring to Table 15-3, suppose the chemist decides to use a t test to determine if the linear term is significant. The value of the test statistic is ________.
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40
One of the consequences of collinearity in multiple regression is biased estimates on the slope coefficients.
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41
TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, there is reason to suspect collinearity between some pairs of predictors.
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, there is reason to suspect collinearity between some pairs of predictors.
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42
TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the residual plot suggests that a nonlinear model on % attendance may be a better model.
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the residual plot suggests that a nonlinear model on % attendance may be a better model.
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43
In data mining where huge data sets are being explored to discover relationships among a large number of variables, the best-subsets approach is more practical than the stepwise regression approach.
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44
An independent variable Xⱼ is considered highly correlated with the other independent variables if
A) VIFⱼ < 5.
B) VIFⱼ > 5.
C) VIFⱼ < VIFᵢ for i ≠ j.
D) VIFⱼ > VIFᵢ for i ≠ j.
A) VIFⱼ < 5.
B) VIFⱼ > 5.
C) VIFⱼ < VIFᵢ for i ≠ j.
D) VIFⱼ > VIFᵢ for i ≠ j.
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45
TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the better model using a 5% level of significance derived from the "best" model above is
A) X₁.
B) X₃.
C) X₁,X₃.
D) X₁,X₂,X₃.
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the better model using a 5% level of significance derived from the "best" model above is
A) X₁.
B) X₃.
C) X₁,X₃.
D) X₁,X₂,X₃.
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46
TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, what are, respectively, the values of the variance inflationary factor of the 3 predictors?
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, what are, respectively, the values of the variance inflationary factor of the 3 predictors?
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47
The ________ (larger/smaller) the value of the Variance Inflationary Factor, the higher is the collinearity of the X variables.
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48
Using the Cp statistic in model building, all models with Cp ≤ (k + 1) are equally good.
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49
The logarithm transformation can be used
A) to overcome violations to the autocorrelation assumption.
B) to test for possible violations to the autocorrelation assumption.
C) to overcome violations to the homoscedasticity assumption.
D) to test for possible violations to the homoscedasticity assumption.
A) to overcome violations to the autocorrelation assumption.
B) to test for possible violations to the autocorrelation assumption.
C) to overcome violations to the homoscedasticity assumption.
D) to test for possible violations to the homoscedasticity assumption.
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50
A regression diagnostic tool used to study the possible effects of collinearity is ________.
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51
TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, which of the following predictors should first be dropped to remove collinearity?
A) X₁
B) X₂
C) X₃
D) None of the above
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, which of the following predictors should first be dropped to remove collinearity?
A) X₁
B) X₂
C) X₃
D) None of the above
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52
The stepwise regression approach takes into consideration all possible models.
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53
TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, which of the following models should be taken into consideration using the Mallows' Cp statistic?
A) X₁,X₃
B) X₁,X₂,X₃
C) Both of the above
D) None of the above
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, which of the following models should be taken into consideration using the Mallows' Cp statistic?
A) X₁,X₃
B) X₁,X₂,X₃
C) Both of the above
D) None of the above
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54
The logarithm transformation can be used
A) to overcome violations to the autocorrelation assumption.
B) to test for possible violations to the autocorrelation assumption.
C) to change a nonlinear model into a linear model.
D) to change a linear independent variable into a nonlinear independent variable.
A) to overcome violations to the autocorrelation assumption.
B) to test for possible violations to the autocorrelation assumption.
C) to change a nonlinear model into a linear model.
D) to change a linear independent variable into a nonlinear independent variable.
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55
TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the "best" model chosen using the adjusted R-square statistic is
A) X₁,X₃.
B) X₁,X₂,X₃.
C) Either of the above
D) None of the above
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the "best" model chosen using the adjusted R-square statistic is
A) X₁,X₃.
B) X₁,X₂,X₃.
C) Either of the above
D) None of the above
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56
In stepwise regression, an independent variable is not allowed to be removed from the model once it has entered into the model.
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57
TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the "best" model using a 5% level of significance among those chosen by the Cp statistic is
A) X₁,X₃.
B) X₁,X₂,X₃.
C) Either of the above
D) None of the above
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the "best" model using a 5% level of significance among those chosen by the Cp statistic is
A) X₁,X₃.
B) X₁,X₂,X₃.
C) Either of the above
D) None of the above
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58
Which of the following will not change a nonlinear model into a linear model?
A) Quadratic regression model
B) Logarithmic transformation
C) Square-root transformation
D) Variance inflationary factor
A) Quadratic regression model
B) Logarithmic transformation
C) Square-root transformation
D) Variance inflationary factor
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59
The goals of model building are to find a good model with the fewest independent variables that is easier to interpret and has lower probability of collinearity.
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60
Using the best-subsets approach to model building, models are being considered when their
A) Cp > k.
B) Cp ≤ k.
C) Cp > (k + 1).
D) Cp ≤ (k + 1).
A) Cp > k.
B) Cp ≤ k.
C) Cp > (k + 1).
D) Cp ≤ (k + 1).
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61
TABLE 15-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Age?
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Age?
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62
TABLE 15-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Head?
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Head?
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63
TABLE 15-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, the variable X₃ should be dropped to remove collinearity.
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, the variable X₃ should be dropped to remove collinearity.
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64
TABLE 15-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, the variable X₂ should be dropped to remove collinearity.
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, the variable X₂ should be dropped to remove collinearity.
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65
TABLE 15-5
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The coefficient of multiple determination (R) for the regression model using each of the 5 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, there is reason to suspect collinearity between some pairs of predictors based on the values of the variance inflationary factor.
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The coefficient of multiple determination (R) for the regression model using each of the 5 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, there is reason to suspect collinearity between some pairs of predictors based on the values of the variance inflationary factor.
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66
TABLE 15-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, there is reason to suspect collinearity between some pairs of predictors based on the values of the variance inflationary factor.
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, there is reason to suspect collinearity between some pairs of predictors based on the values of the variance inflationary factor.
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67
TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, what is the value of the test statistic to determine whether the quadratic effect of daily average of the percentage of students attending class on percentage of students passing the proficiency test is significant at a 5% level of significance?
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, what is the value of the test statistic to determine whether the quadratic effect of daily average of the percentage of students attending class on percentage of students passing the proficiency test is significant at a 5% level of significance?
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68
TABLE 15-5
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The coefficient of multiple determination (R) for the regression model using each of the 5 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, what is the value of the variance inflationary factor of Cargo Vol?
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The coefficient of multiple determination (R) for the regression model using each of the 5 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, what is the value of the variance inflationary factor of Cargo Vol?
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69
TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the null hypothesis should be rejected when testing whether the quadratic effect of daily average of the percentage of students attending class on percentage of students passing the proficiency test is significant at a 5% level of significance.
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the null hypothesis should be rejected when testing whether the quadratic effect of daily average of the percentage of students attending class on percentage of students passing the proficiency test is significant at a 5% level of significance.
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70
TABLE 15-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Edu?
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Edu?
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71
TABLE 15-5
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The coefficient of multiple determination (R) for the regression model using each of the 5 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, what is the value of the variance inflationary factor of SUV?
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The coefficient of multiple determination (R) for the regression model using each of the 5 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, what is the value of the variance inflationary factor of SUV?
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72
TABLE 15-5
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The coefficient of multiple determination (R) for the regression model using each of the 5 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, what is the value of the variance inflationary factor of Sedan?
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The coefficient of multiple determination (R) for the regression model using each of the 5 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, what is the value of the variance inflationary factor of Sedan?
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73
TABLE 15-5
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The coefficient of multiple determination (R) for the regression model using each of the 5 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, what is the value of the variance inflationary factor of MPG?
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The coefficient of multiple determination (R) for the regression model using each of the 5 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, what is the value of the variance inflationary factor of MPG?
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74
TABLE 15-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Job Yr?
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Job Yr?
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75
TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, what is the p-value of the test statistic to determine whether the quadratic effect of daily average of the percentage of students attending class on percentage of students passing the proficiency test is significant at a 5% level of significance?
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, what is the p-value of the test statistic to determine whether the quadratic effect of daily average of the percentage of students attending class on percentage of students passing the proficiency test is significant at a 5% level of significance?
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76
TABLE 15-5
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The coefficient of multiple determination (R) for the regression model using each of the 5 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, what is the value of the variance inflationary factor of HP?
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The coefficient of multiple determination (R) for the regression model using each of the 5 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, what is the value of the variance inflationary factor of HP?
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77
TABLE 15-4
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the quadratic effect of daily average of the percentage of students attending class on percentage of students passing the proficiency test is not significant at a 5% level of significance.
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):
Referring to Table 15-4, the quadratic effect of daily average of the percentage of students attending class on percentage of students passing the proficiency test is not significant at a 5% level of significance.
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78
TABLE 15-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Married?
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Married?
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79
TABLE 15-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Manager?
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, what is the value of the variance inflationary factor of Manager?
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80
TABLE 15-6
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, the variable X₁ should be dropped to remove collinearity.
Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y) and the independent variables are the age of the worker (X₁), the number of years of education received (X₂), the number of years at the previous job (X₃), a dummy variable for marital status (X₄: 1 = married, 0 = otherwise), a dummy variable for head of household (X₅: 1 = yes, 0 = no) and a dummy variable for management position (X₆: 1 = yes, 0 = no).
The coefficient of multiple determination (R) for the regression model using each of the 6 variables Xⱼ as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993.
The partial results from best-subset regression are given below:
Referring to Table 15-6, the variable X₁ should be dropped to remove collinearity.
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Unlock Deck
Unlock for access to all 96 flashcards in this deck.
