Exam 15: Multiple Regression Model Building

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 X₃ should be dropped to remove collinearity?

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.

One of the consequences of collinearity in multiple regression is biased estimates on the slope coefficients.

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,X₂,X₃,X₅ and X₆ should be among the appropriate models using the Mallow's C_p statistic.

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.

The logarithm transformation can be used

Which of the following regression procedures are needed when the dependent variable is categorical?

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,X₂,X₅ and X₆ should be among the appropriate models using the Mallow's C_p statistic.

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 Manager?

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 X₅ should be dropped to remove collinearity?

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 HP?

Collinearity is present when there is a high degree of correlation between independent variables.

The Variance Inflationary Factor (VIF)measures the correlation of the X variables with the Y variable.

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?

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 Head?

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 selected using the adjusted r² statistic.

The C_p statistic is used

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

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 the six independent variables should be among the appropriate models using the Mallow's C_p statistic.

The parameter estimates are biased when collinearity is present in a multiple regression equation.