Exam 15: Multiple Regression Model Building

A regression diagnostic tool used to study the possible effects of collinearity is ________.

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.

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 model that includes X₁, X₂, X₃, X₅ and X₆ should be selected using the adjusted r² statistic.

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?

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 Mallow's Cp statistic for the model that includes all the six independent variables?

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 Mallow's Cp statistic for the model that includes X₁, X₂, X₅ and X₆?

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 ________.

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.

An independent variable Xⱼ is considered highly correlated with the other independent variables if

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 ________.

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 X₅ should be dropped to remove collinearity.

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.

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)?

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.

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.

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 X₆ should be dropped to remove collinearity.