Deck 15: Multiple Regression Model Building

Question 1

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

Answer 1

False

Question 2

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.

Answer 2

True

Question 3

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

Answer 3

True

Question 4

As a project for his business statistics class,a student examined the factors that determined parking meter rates throughout the campus area.Data were collected for the price per hour of parking,blocks to the quadrangle,and one of the three jurisdictions: on campus,in downtown and off campus,or outside of downtown and off campus.The population regression model hypothesized is Y_i = $\beta$ ₀ + $\beta$ ₁ X_1i + $\beta$ ₂ X _2i + $\beta$ ₃ X_3i + $\varepsilon$
Where
Y is the meter price
X₁ is the number of blocks to the quad
X₂ is a dummy variable that takes the value 1 if the meter is located in downtown and off campus and the value 0 otherwise
X₃ is a dummy variable that takes the value 1 if the meter is located outside of downtown and off campus,and the value 0 otherwise
Suppose that whether the meter is located on campus is an important explanatory factor.Why should the variable that depicts this attribute not be included in the model?

A)Its inclusion will introduce autocorrelation.
B)Its inclusion will introduce collinearity.
C)Its inclusion will inflate the standard errors of the estimated coefficients.
D)Both (b)and (c).

Question 5

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

Question 6

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

Question 7

Collinearity is present if the dependent variable is linearly related to one of the explanatory variables.

Question 8

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

Question 9

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

A)the slope.
B)the Y-intercept.
C)the VIF.
D)the standard error of the estimate.

Question 10

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?

A)Randomness of error terms
B)Collinearity
C)Normality of residuals
D)Missing observations

Question 11

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.

Question 12

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

Question 13

Which of the following is used to find a "best" model?

A)Odds ratio
B)Mallow's C_p
C)Standard error of the estimate
D)SST

Question 14

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

A)forward selection
B)residual analysis
C)backward elimination
D)stepwise regression

Question 15

One of the consequences of collinearity in multiple regression is inflated standard errors in some or all of the estimated slope coefficients.

Question 16

The C_p statistic is used

A)to determine if there is a problem of collinearity.
B)if the variances of the error terms are all the same in a regression model.
C)to choose the best model.
D)to determine if there is an irregular component in a time series.

Question 17

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.

Question 18

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

A)autocorrelation.
B)the presence of dummy variables.
C)the absence of dummy variables.
D)collinearity.

Question 19

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?

A)Randomness of error terms
B)Collinearity
C)Normality of residuals
D)Missing observations

Question 20

The Variance Inflationary Factor (VIF)measures the

A)correlation of the X variables with the Y variable.
B)correlation of the X variables with each other.
C)contribution of each X variable with the Y variable after all other X variables are included in the model.
D)standard deviation of the slope.

Question 21

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

A)VIF_j $\lt$ 5
B)VIF_j $\gt$ 5
C)VIF_j $\lt$ VIF_i For i $\neq$ j
D)VIF_j $\gt$ VIF_i For i $\neq$ j

Question 22

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

Question 23

Using the C_p statistic in model building,all models with C_p $\le$ (K+1)are equally good.

Question 24

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.

Question 25

The logarithm transformation can be used

A)to overcome violations to the autocorrelation assumption.
B)to test for possible violations to the autocorrelation assumption.
C)to overcome violations to the homoscedasticity assumption.
D)to test for possible violations to the homoscedasticity assumption.

Question 26

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

Question 27

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?

Question 28

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?

Question 29

The logarithm transformation can be used

A)to overcome violations to the autocorrelation assumption.
B)to test for possible violations to the autocorrelation assumption.
C)to change a nonlinear model into a linear model.
D)to change a linear independent variable into a nonlinear independent variable.

Question 30

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.

Question 31

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?

Question 32

The _____ (larger/smaller)the value of the Variance Inflationary Factor,the higher is the collinearity of the X variables.

Question 33

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?

Question 34

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

A)C_p $\gt$ k
B)C_p $\le$ k
C)C_p $\gt$ (K+1)
D)C_p $\le$ (K+1)

Question 35

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?

Question 36

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.

Question 37

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

Question 38

The stepwise regression approach takes into consideration all possible models.

Question 39

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?

Question 40

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 Edu?

Question 41

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?

Question 42

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?

Question 43

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?

Question 44

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?

Question 45

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?

Question 46

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.

Question 47

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

Question 48

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?

Question 49

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 X₂ should be dropped to remove collinearity?

Question 50

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,X₅ and X₆?

Question 51

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?

Question 52

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,X₅ and X₆?

Question 53

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

Question 54

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 X₆ should be dropped to remove collinearity?

Question 55

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.

Question 56

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 X₄ should be dropped to remove collinearity?

Question 57

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?

Question 58

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?

Question 59

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?

Question 60

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.

Question 61

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

A)12
B)16
C)15
D)14

Question 62

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

A)Evaluate alternate models using best subsets regression.
B)Evaluate interaction and quadratic terms.
C)Use logistic regression in lieu of least squares regression.
D)Validate the model before implementing it.

Question 63

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.

Question 64

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.

Question 65

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 selected using the adjusted r² statistic.

Question 66

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.

Question 67

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

A)principle of parsimony
B)cross validation
C)stepwise regression
D)collecting new data and using regression to validate the model.