Exam 15: Multiple Regression Model Building

SCENARIO 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 ²_j)for the regression model using each of the 5 variables X _j 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 Scenario 15-5,what is the value of the variance inflationary factor of Sedan?

SCENARIO 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 ²_j )for the regression model using each of the 6 variables X _j 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 Scenario 15-6,the variable X₁ should be dropped to remove collinearity?

Collinearity will result in excessively low standard errors of the parameter estimates reported in the regression output.

SCENARIO 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 ²_j )for the regression model using each of the 6 variables X _j 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 Scenario 15-6,what is the value of the variance inflationary factor of Job Yr?

SCENARIO 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 ²_j )for the regression model using each of the 6 variables X _j 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 Scenario 15-6,what is the value of the Mallow's C_p statistic for the model that includes all the six independent variables?

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

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