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Exam 15: Multiple Regression Model Building

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Question 31

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

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Question 32

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

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The logarithm transformation can be used

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 0.05,she would decide that the linear model is sufficient.

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 15-5 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 )for the regression model using each of the 5 variables Xⱼ 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 Table 15-5,what is the value of the variance inflationary factor of MPG?

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

Which of the following will not change a nonlinear model into a linear model?

Collinearity is present when there is a high degree of correlation between the dependent variable and any of the 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 (R²_J )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.

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.

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 (R²_J )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 variance inflationary factor of Married?

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.If she chooses to use a level of significance of 0.01 she would decide that there is a significant curvilinear relationship.

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 (R²_J )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,X₅ and X₆ should be selected using the adjusted r² statistic.

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

Using the Cp statistic in model building,all models with Cp ≤ (k + 1)are equally good.

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 (R²_J )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 X₃ should be dropped to remove collinearity.

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 the linear term is significant.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 (R²_J )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.

A high value of R² significantly above 0 in multiple regression accompanied by insignificant t-values on all parameter estimates very often indicates a high correlation between independent variables in the model.