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 SUV?

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 Cargo Vol?

If a group of independent variables are not significant individually but are significant as a group at a specified level of significance,this is most likely due to

Which of the following precautions regression procedures in model selection is an attempt to find the best regression model without examining all possible models?

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 X₁,X₂,X₃,X₅ and X₆?

In stepwise regression,an independent variable is not allowed to be removed from the model once it has entered into the model.

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.

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?

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 model that includes all six independent variables should be selected using the adjusted r² statistic.

With four independent variables in a proposed regression model,how many models would need to be evaluated in a best subsets approach?

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,there is reason to suspect collinearity between some pairs of predictors based on the values of the variance inflationary factor.

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 model that includes X₁,X₅ and X₆ should be among the appropriate models using the Mallow's C_p statistic.

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

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 X₁,X₃,X₅ and X₆?

Using the best-subsets approach to model building,models are being considered when their

Collinearity is present when there is a high degree of correlation between the dependent variable and any of the independent variables.

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 MPG?

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 Married?

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 Age?

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