Instruction 16-6 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 (XS1U1B11S1U1B0), the number of years of education received (XS1U1B12S1U1B0), the number of years at the previous job (XS1U1B13S1U1B0), a dummy variable for marital status (XS1U1B14S1U1B0: 1 = married, 0 = otherwise), a dummy variable for head of household (XS1U1B15S1U1B0: 1 = yes, 0 = no) and a dummy variable for management position (XS1U1B16S1U1B0: 1 = yes, 0 = no). The coefficient of multiple determination (RS1U1P12S1S1P0S1U1B1jS1U1B0) the regression model using each of the 6 variables XS1U1B1j S1U1B0as 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: \[\begin{array} { | l | l | l | l | } \hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\ \hline X _ { 1 } X _ { 5 } X _ { 6 } & 0.4568 & 0.4116 & 18.3534 \\ \hline X _ { 1 } X _ { 2 } X _ { 5 } X _ { 6 } & 0.4697 & 0.4091 & 18.3919 \\ \hline X _ { 1 } X _ { 3 } X _ { 5 } X _ { 6 } & 0.4691 & 0.4084 & 18.4023 \\ \hline X _ { 1 } X _ { 2 } X _ { 3 } X _ { 5 } X _ { 6 } & 0.4877 & 0.4123 & 18.3416 \\ \hline X _ { 1 } X _ { 2 } X _ { 3 } X _ { 4 } X _ { 5 } X _ { 6 } & 0.4949 & 0.4030 & 18.4861 \\ \hline \end{array}\] -Referring to Instruction 16-6,what is the value of the variance inflationary factor of Married?

The answer of Instruction 16-6 Given below are results from the...

A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesise 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: \[Y = B _ { 0 } + B _ { 1 } X + B_ { 2 } X ^ { 2 } + \varepsilon\] where Y = demand (in thousands) and X = retail price per carat. \[\begin{array} { | l | l | l | l | l | l | } \hline \text { SUMMARY } & \text { OUTPUT } & & & & \\ \hline \text { Regression } & \text { Statistics } & & & & \\ \hline \text { Multiple R } & & 0.994 & & & \\ \hline \text { R Square } & & 0.988 & & & \\ \hline \text { Std. Error } & & 12.42 & & & \\ \hline \text { Observations } & & 12 & & & \\ \hline & & & & & \\ \hline \text { ANOVA } & & & & & \\ \hline & \text { df } & \text { SS } & \text { MS } & \text { F } & \text { Signif F } \\ \hline \text { Regression } & 2 & 115,145 & 57,573 & 373 & 0.0001 \\ \hline \text { Residual } & 9 & 1,388 & 154 & & \\ \hline \text { Total } & 11 & 116,533 & & & \\ \hline & & & & & \\ \hline & \text { Coeff } & \text { Std. Error } & \text { t Stat } & P \text {-Value } & \\ \hline \text { Intercept } & 286.42 & 9.66 & 29.64 & 0.0001 & \\ \hline \text { Price } & - 0.31 & 0.06 & - 5.14 & 0.0006 & \\ \hline \text { Price Sq } & 0.000067 & 0.00007 & 0.95 & 0.3647 & \\ \hline \end{array}\] 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 Instruction 16-1,does the quadratic term appear to be significant in the response curve relating the demand (Y)and the price (X)at 10% level of significance?

A) No, sine the value of ?2 is near 0. B) No, since the p-value for the test is greater than 0.10. C) Yes, since the p-value for the test is less than 0.10. D) Yes, since the value of ?2 is positive. A) No, sine the value of ?2 is near 0. B) No, since the p-value for the test is greater than 0.10. C) Yes, since the p-value for the test is less than 0.10. D) Yes, since the value of ?2 is positive.

Instruction 16-6 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 (XS1U1B11S1U1B0), the number of years of education received (XS1U1B12S1U1B0), the number of years at the previous job (XS1U1B13S1U1B0), a dummy variable for marital status (XS1U1B14S1U1B0: 1 = married, 0 = otherwise), a dummy variable for head of household (XS1U1B15S1U1B0: 1 = yes, 0 = no) and a dummy variable for management position (XS1U1B16S1U1B0: 1 = yes, 0 = no). The coefficient of multiple determination (RS1U1P12S1S1P0S1U1B1jS1U1B0) the regression model using each of the 6 variables XS1U1B1j S1U1B0as 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: \[\begin{array} { | l | l | l | l | } \hline \text { Model } & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\ \hline X _ { 1 } X _ { 5 } X _ { 6 } & 0.4568 & 0.4116 & 18.3534 \\ \hline X _ { 1 } X _ { 2 } X _ { 5 } X _ { 6 } & 0.4697 & 0.4091 & 18.3919 \\ \hline X _ { 1 } X _ { 3 } X _ { 5 } X _ { 6 } & 0.4691 & 0.4084 & 18.4023 \\ \hline X _ { 1 } X _ { 2 } X _ { 3 } X _ { 5 } X _ { 6 } & 0.4877 & 0.4123 & 18.3416 \\ \hline X _ { 1 } X _ { 2 } X _ { 3 } X _ { 4 } X _ { 5 } X _ { 6 } & 0.4949 & 0.4030 & 18.4861 \\ \hline \end{array}\] -Referring to Instruction 16-6,what is the value of the variance inflationary factor of Age?

The answer of Instruction 16-6 Given below are results from the...

Instruction 16-2 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 quadratic model to this data. The results obtained by Microsoft Excel follow. $\begin{array}{|c|c|c|c|c|c|} \hline & \text { OUTPU? } & & & & \\ \hline \text { Regression } & \text { Statistics } & & & & \\ \hline \text { Multiple R } & & 0.747 & & & \\ \hline \text { R Square } & & 0.558 & & & \\ \hline \text { Adj. R Square } & & 0.478 & & & \\ \hline \text { Std. Error } & & 863.1 & & & \\ \hline \text { Observations } & & 14 & & & \\ \hline & & & & & \\ \hline \text { ANOVA } & & & & & \\ \hline & d f & \text { Ss } & \text { MS } & F & \text { Signif F } \\ \hline \text { Regression } & 2 & 10,344,797 & 5,172,399 & 6.94 & 0.0110 \\ \hline \text { Residual } & 11 & 8,193,929 & 744,903 & & \\ \hline \text { Total } & 13 & 18,538,726 & & & \\ \hline & & & & & \\ \hline & \text { Coeff } & \text { Std. Error } & \text { t stat } & P \text {-value } & \\ \hline \text { Intercept } & 1283.0 & 352.0 & 3.65 & 0.0040 & \\ \hline \text { CenDose } & 25.228 & 8.631 & 2.92 & 0.0140 & \\ \hline \text { CenDoseSq } & 0.8604 & 0.3722 & 2.31 & 0.0410 & \\ \hline \end{array}$ Note: Adj. R Square = Adjusted R Square; Std. Error = Standard Error -Referring to Instruction 16-2,suppose the chemist decides to use a t test to determine if there is a significant difference between a quadratic model without a linear term and a quadratic model that includes a linear term.The value of the test statistic is _______.

The answer of Instruction 16-2 A chemist employed by a pharmaceutical...

Exam 16: Multiple Regression Model Building

Instruction 16-6 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 (R²_j) the regression model using each of the 6 variables X_jas 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: Model R Square Adj. R Square Std. Error 0.4568 0.4116 18.3534 0.4697 0.4091 18.3919 0.4691 0.4084 18.4023 0.4877 0.4123 18.3416 0.4949 0.4030 18.4861 -Referring to Instruction 16-6,the model that includes all six independent variablesshould be selected using the Mallow's C_p statistic.

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Question 81

If your data has a non-linear relationship,one transformation that may be useful is the logarithmic transformation.

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Question 82

Calculating Cook's Distance Statistic requires the use of matrix algebra.

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Question 83

In multiple regression,the _______procedure permits variables to enter and leave the model at different stages of its development.

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Question 84

Instruction 16-6 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 (R²_j) the regression model using each of the 6 variables X_jas 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: Model R Square Adj. R Square Std. Error 0.4568 0.4116 18.3534 0.4697 0.4091 18.3919 0.4691 0.4084 18.4023 0.4877 0.4123 18.3416 0.4949 0.4030 18.4861 -Referring to Instruction 16-6,what is the value of the variance inflationary factor of Married?

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Question 85

A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesise 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: $Y = B _ { 0 } + B _ { 1 } X + B_ { 2 } X ^ { 2 } + \varepsilon$ where Y = demand (in thousands) and X = retail price per carat. SUMMARY OUTPUT Regression Statistics Multiple R 0.994 R Square 0.988 Std. Error 12.42 Observations 12 ANOVA df SS MS F Signif F Regression 2 115,145 57,573 373 0.0001 Residual 9 1,388 154 Total 11 116,533 Coeff Std. Error t Stat P -Value Intercept 286.42 9.66 29.64 0.0001 Price -0.31 0.06 -5.14 0.0006 Price Sq 0.000067 0.00007 0.95 0.3647 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 Instruction 16-1,does the quadratic term appear to be significant in the response curve relating the demand (Y)and the price (X)at 10% level of significance?

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Question 86

Instruction 16-6 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 (R²_j) the regression model using each of the 6 variables X_jas 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: Model R Square Adj. R Square Std. Error 0.4568 0.4116 18.3534 0.4697 0.4091 18.3919 0.4691 0.4084 18.4023 0.4877 0.4123 18.3416 0.4949 0.4030 18.4861 -Referring to Instruction 16-6,what is the value of the variance inflationary factor of Age?

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Question 87

For a model with 3 independent variables and data set with 75 observations,the denominator degrees of freedom for the Cook's Distance Statistic would be 70.

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Question 88

Instruction 16-6 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 (R²_j) the regression model using each of the 6 variables X_jas 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: Model R Square Adj. R Square Std. Error 0.4568 0.4116 18.3534 0.4697 0.4091 18.3919 0.4691 0.4084 18.4023 0.4877 0.4123 18.3416 0.4949 0.4030 18.4861 -Referring to Instruction 16-6,what is the value of the Mallow's C_p statistic for the model that includes X₁,X₂,X₃,X₅ and X₆?

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Question 89

Which of the following is NOT used to determine observations that have influential effect on the fitted model?

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Question 90

Instruction 16-2 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 quadratic model to this data. The results obtained by Microsoft Excel follow. OUTPU? Regression Statistics Multiple R 0.747 R Square 0.558 Adj. R Square 0.478 Std. Error 863.1 Observations 14 ANOVA df Ss MS F Signif F Regression 2 10,344,797 5,172,399 6.94 0.0110 Residual 11 8,193,929 744,903 Total 13 18,538,726 Coeff Std. Error t stat P -value Intercept 1283.0 352.0 3.65 0.0040 CenDose 25.228 8.631 2.92 0.0140 CenDoseSq 0.8604 0.3722 2.31 0.0410 Note: Adj. R Square = Adjusted R Square; Std. Error = Standard Error -Referring to Instruction 16-2,suppose the chemist decides to use a t test to determine if there is a significant difference between a quadratic model without a linear term and a quadratic model that includes a linear term.The value of the test statistic is _______.

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Question 91

Instruction 16-6 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 (R²_j) the regression model using each of the 6 variables X_jas 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: Model R Square Adj. R Square Std. Error 0.4568 0.4116 18.3534 0.4697 0.4091 18.3919 0.4691 0.4084 18.4023 0.4877 0.4123 18.3416 0.4949 0.4030 18.4861 -Referring to Instruction 16-6,what is the value of the Mallow's C_p statistic for the model that includes X₁,X₅ and X₆?

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Question 92

Evaluating the influence of individual data points using a studentised deleted residual test is usually done with a one-tailed t-test.

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Question 93

If your data has a non-linear relationship,one transformation that may be useful is the logarithmic transformation.

Calculating Cook's Distance Statistic requires the use of matrix algebra.

In multiple regression,the _______procedure permits variables to enter and leave the model at different stages of its development.

For a model with 3 independent variables and data set with 75 observations,the denominator degrees of freedom for the Cook's Distance Statistic would be 70.

Which of the following is NOT used to determine observations that have influential effect on the fitted model?

Evaluating the influence of individual data points using a studentised deleted residual test is usually done with a one-tailed t-test.

Defining and Collecting Data

Organising and Visualising Data

Numerical Descriptive Measures

Basic Probability

Some Important Discrete Probability Distributions

The Normal Distribution and Other Continuous Distributions

Sampling Distributions

Confidence Interval Estimation

Fundamentals of Hypothesis Testing: One-Sample Tests

Hypothesis Testing: Two-Sample Tests

Analysis of Variance

Simple Linear Regression

Introduction to Multiple Regression

Time-Series Forecasting and Index Numbers

Chi-Square Tests

Decision Making

Statistical Applications in Quality Management

Further Non-Parametric Tests

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