Deck 14: Building Multiple Regression Models

Question 1

The interaction between two independent variables can be examined by including a new variable, which is the sum of the two independent variables, in the regression model.

Answer 1

False

Question 2

Regression models in which the highest power of any predictor variable is 1 and in which there are no cross product terms are referred to as first-order models.

Answer 2

True

Question 3

If the effect of an independent variable (e.g., humidity)on a dependent variable (e.g., hardness)is affected by different ranges of values for a second independent variable (e.g., temperature), the two independent variables are said to interact.

Answer 3

True

Question 4

A logarithmic transformation may be applied to both positive and negative numbers.

Question 5

If a square root transformation is applied to a series of positive numbers greater than 1, the numerical values of the numbers in the transformed series will be smaller than the corresponding numbers in the original series.

Question 6

If two or more independent variables are highly correlated, the regression analysis might suffer from the problem of multicollinearity.

Question 7

A linear regression model cannot be used to explore the possibility that a quadratic relationship may exist between two variables.

Question 8

If a data set contains k independent variables, the "all possible regression" search procedure will determine 2^k different models.

Question 9

If a qualitative variable has c categories, then only (c - 1)dummy variables must be included in the regression model.

Question 10

The regression model is called a quadratic model.

Question 11

The regression model y = $\beta$ ₀ + $\beta$ ₁ x₁ + $\beta$ ₂ x₂ + $\beta$ ₃ x₃ + $\varepsilon$ is a third order model.

Question 12

The regression model y = $\beta$ ₀ + $\beta$ ₁ x₁ + $\beta$ ₂ x₂ + $\beta$ ₃ x₁x₂ + $\varepsilon$ is a first-order model.

Question 13

If a qualitative variable has c categories, then c dummy variables must be included in the regression model, one for each category.

Question 14

A useful tool in improving the regression model fit is recoding data.

Question 15

If a square transformation is applied to a series of positive numbers greater than 1, the numerical values of the numbers in the transformed series will be smaller than the corresponding numbers in the original series.

Question 16

Stepwise regression is one of the ways to prevent the problem of multicollinearity.

Question 17

Qualitative data cannot be incorporated into linear regression models.

Question 18

If a data set contains k independent variables, the "all possible regression" search procedure will determine 2^k - 1 different models.

Question 19

A qualitative variable which represents categories such as geographical territories or job classifications may be included in a regression model by using indicator or dummy variables.

Question 20

A linear regression model can be used to explore the possibility that a quadratic relationship may exist between two variables by suitably transforming the independent variable.

Question 21

The following scatter plot indicates that ___.

A)a log x transform may be useful
B)a log y transform may be useful
C)a x² transform may be useful
D)no transform is needed
E)a 1/x transform may be useful

Question 22

A multiple regression analysis produced the following tables: Using $\alpha$ = 0.01 to test the null hypothesis H₀: $\beta$ ₁ = $\beta$ ₂ = 0, the critical F value is ___.

A)5.42
B)5.49
C)7.60
D)3.35
E)2.49

Question 23

A multiple regression analysis produced the following tables: Using $\alpha$ = 0.05 to test the null hypothesis H₀: $\beta$ ₁ = 0, the critical t value is ___.

A)± 1.311
B)± 1.699
C)± 1.703
D)± 2.502
E)± 2.052

Question 24

A multiple regression analysis produced the following tables: These results indicate that ___.

A)none of the predictor variables is significant at the 5% level
B)each predictor variable is significant at the 5% level
C)x₁ is the only predictor variable significant at the 5% level
D)x₁² is the only predictor variable significant at the 5% level
E)each predictor variable is insignificant at the 5% level

Question 25

A multiple regression analysis produced the following tables: The regression equation for this analysis is ___.

A)y = 762.1533 + 96.8433 x₁ + 3.007943 x₁²
B)y = 1411.876 + 762.1533 x₁ + 1.852483 x₁²
C)y = 1411.876 + 35.18215 x₁ + 7.721648 x₁²
D)y = 762.1533 + 1.852483 x₁ + 0.074919 x₁²
E)y = 762.1533 - 1.852483 x₁ + 0.074919 x₁²

Question 26

The following scatter plot indicates that ___.

A)a log x transform may be useful
B)a log y transform may be useful
C)an x² transform may be useful
D)no transform is needed
E)a (- x)transform may be useful

Question 27

A multiple regression analysis produced the following tables: The sample size for this analysis is ___.

A)28
B)25
C)30
D)27
E)2

Question 28

A multiple regression analysis produced the following tables: Using $\alpha$ = 0.05 to test the null hypothesis H₀: $\beta$ ₂ = 0, the critical t value is ___.

A)± 1.311
B)± 1.699
C)± 1.703
D)± 2.052
E)± 2.502

Question 29

A multiple regression analysis produced the following tables: Using $\alpha$ = 0.05 to test the null hypothesis H₀: $\beta$ ₁ = $\beta$ ₂ = 0, the critical F value is ___.

A)4.24
B)3.39
C)5.57
D)3.35
E)2.35

Question 30

A multiple regression analysis produced the following tables: The sample size for this analysis is ___.

A)27
B)29
C)30
D)25
E)28

Question 31

A multiple regression analysis produced the following tables: For x₁= 10, the predicted value of y is ___.

A)1,632.02
B)1,928.24
C)10.23
D)314.97
E)938.35

Question 32

The following scatter plot indicates that ___.

A)a x² transform may be useful
B)a log y transform may be useful
C)a x⁴ transform may be useful
D)no transform is needed
E)a x³ transform may be useful

Question 33

A multiple regression analysis produced the following tables: Using $\alpha$ = 0.10 to test the null hypothesis H₀: $\beta$ ₂ = 0, the critical t value is ___.

A)± 1.316
B)± 1.314
C)± 1.703
D)± 1.780
E)± 1.708

Question 34

The following scatter plot indicates that ___.

A)a log x transform may be useful
B)a y² transform may be useful
C)a x² transform may be useful
D)no transform is needed
E)a 1/x transform may be useful

Question 35

Multiple linear regression models can handle certain nonlinear relationships by ___.

A)biasing the sample
B)recoding or transforming variables
C)adjusting the resultant ANOVA table
D)adjusting the observed t and F values
E)performing nonlinear regression

Question 36

A multiple regression analysis produced the following tables: For x₁= 10, the predicted value of y is ___.

A)8.88
B)2,031.38
C)253.86
D)262.19
E)2,535.86

Question 37

A multiple regression analysis produced the following tables: Using $\alpha$ = 0.10 to test the null hypothesis H₀: $\beta$ ₁ = 0, the critical t value is ___.

A)± 1.316
B)± 1.314
C)± 1.703
D)± 1.780
E)± 1.708

Question 38

A multiple regression analysis produced the following tables: The regression equation for this analysis is ___.

A)y = 707.9144 + 2.903307 x₁ + 11.91297 x₁²
B)y = 707.9144 + 435.1183 x₁ + 1.626947 x₁²
C)y = 435.1183 + 81.62802 x₁ + 3.806211 x₁²
D)y = 1.626947 + 0.035568 x₁ + 3.129878 x₁²
E)y = 1.626947 + 0.035568 x₁ - 3.129878 x₁²

Question 39

A multiple regression analysis produced the following tables: For x₁= 20, the predicted value of y is ___.

A)5531.17
B)1,928.25
C)1023.05
D)3149.75
E)9380.35

Question 40

A multiple regression analysis produced the following tables: For x₁= 20, the predicted value of y is ___.

A)5,204.18
B)2,031.38
C)2,538.86
D)6262.19
E)6,535.86

Question 41

Alan Ho, a market analyst for Clear Sound Inc., is analyzing sales of heavy metal CD's.Alan's dependent variable is annual heavy metal CD sales (in $1,000,000's), and his independent variables are teenage population (in 1,000's)and type of sales district (0 = urban, 1 = rural).Regression analysis of the data yielded the following tables: Alan's model is ___.

A)y = 1.7 + 0.384212 x₁ + 4.424638 x₂ + 0.00166 x₃
B)y = 1.7 + 0.04 x₁ + 1.5666667 x₂
C)y = 0.384212 + 0.014029 x₁ + 0.20518 x₂
D)y = 4.424638 + 2.851146 x₁ - 7.63558 x₂
E)y = 1.7 + 0.04 x₁ - 1.5666667 x₂

Question 42

Which of the following iterative search procedures for model building in a multiple regression analysis adds variables to the model as it proceeds, but does not re-evaluate the contribution of previously entered variables?

A)backward elimination
B)stepwise regression
C)forward selection
D)all possible regressions
E)forward elimination

Question 43

Alan Ho, a market analyst for Clear Sound Inc., is analyzing sales of heavy metal CD's.Alan's dependent variable is annual heavy metal CD sales (in $1,000,000's), and his independent variables are teenage population (in 1,000's)and type of sales district (0 = urban, 1 = rural).Regression analysis of the data yielded the following tables: For an urban sales district with 10,000 teenagers, Alan's model predicts annual sales of heavy metal CD sales of ___.

A)$2,100,000
B)$524,507
C)$533,333
D)$729,683
E)$21,000,000

Question 44

Abby Ross, a market specialist at the market research firm of Saez, Gann, and Spitz, is analyzing household budget data collected by her firm.Abby's dependent variable is monthly household expenditures on groceries (in $'s), and her independent variables are annual household income (in $1,000's)and household neighbourhood (0 = suburban, 1 = rural).Regression analysis of the data yielded the following table: For a rural household with $70,000 annual income, Abby's model predicts monthly grocery expenditure of ___.

A)$141.15
B)$190.28
C)$164.52
D)$122.67
E)$132.28

Question 45

Alan Ho, a market analyst for Clear Sound Inc., is analyzing sales of heavy metal CD's.Alan's dependent variable is annual heavy metal CD sales (in $1,000,000's), and his independent variables are teenage population (in 1,000's)and type of sales district (0 = urban, 1 = rural).Regression analysis of the data yielded the following tables: For two sales districts with the same number of teenagers one urban and one rural, Alan's model predicts ___.

A)$1,566,666 higher sales in the rural district
B)the same sales in both districts
C)$1,566,666 lower sales in the rural district
D)$1,700,000 higher sales in the urban district
E)$ 1,700,000 lower sales in the rural district

Question 46

In multiple regression analysis, qualitative variables are sometimes referred to as ___.

A)dummy variables
B)quantitative variables
C)dependent variables
D)performance variables
E)cardinal variables

Question 47

Alan Ho, a market analyst for Clear Sound Inc., is analyzing sales of heavy metal CD's.Alan's dependent variable is annual heavy metal CD sales (in $1,000,000's), and his independent variables are teenage population (in 1,000's)and type of sales district (0 = urban, 1 = rural).Regression analysis of the data yielded the following tables: For a rural sales district with 10,000 teenagers, Alan's model predicts annual sales of heavy metal CD sales of ___.

A)$2,100,000
B)$524,507
C)$533,333
D)$729,683
E)$210,000

Question 48

Hope Williams, Marketing Manager of RightAid Pharmacy, Inc., wants a regression model to predict sales in the greeting card department.Her data set includes two qualitative variables: the pharmacy neighbourhood (urban, suburban, and rural), and lighting level in the greeting card department (soft, medium, and bright).The number of dummy variables needed for "lighting level" in Hope's regression model is ___.

A)1
B)2
C)3
D)4
E)5

Question 49

Abby Ross, a market specialist at the market research firm of Saez, Gann, and Spitz, is analyzing household budget data collected by her firm.Abby's dependent variable is monthly household expenditures on groceries (in $'s), and her independent variables are annual household income (in $1,000's)and household neighbourhood (0 = suburban, 1 = rural).Regression analysis of the data yielded the following table: For two households, one suburban and one rural, Abby's model predicts ___.

A)equal monthly expenditures for groceries
B)the suburban household's monthly expenditures for groceries will be $49 more
C)the rural household's monthly expenditures for groceries will be $49 more
D)the suburban household's monthly expenditures for groceries will be $8 more
E)the rural household's monthly expenditures for groceries will be $49 less

Question 50

Hope Williams, Marketing Manager of RightAid Pharmacy, Inc., wants a regression model to predict sales in the greeting card department.Her data set includes two qualitative variables: the pharmacy neighbourhood (urban, suburban, and rural), and lighting level in the greeting card department (soft, medium, and bright).The number of dummy variables needed for Hope's regression model is ___.

A)2
B)4
C)6
D)8
E)9

Question 51

If a qualitative variable has 4 categories, how many dummy variables must be created and used in the regression analysis?

A)3
B)4
C)5
D)6
E)7

Question 52

Yvonne Lang, VP of Finance at Digital Components, Inc.(DCI), wants a regression model which predicts the average collection period on credit sales.Her data set includes two qualitative variables: sales discount rates (0%, 2%, 4%, and 6%), and total assets of credit customers (small, medium, and large).The number of dummy variables needed for "sales discount rate" in Yvonne's regression model is ___.

A)1
B)2
C)3
D)4
E)7

Question 53

Which of the following iterative search procedures for model building in a multiple regression analysis starts with all independent variables in the model and then drops nonsignificant independent variables in a step-by-step manner?

A)backward elimination
B)stepwise regression
C)forward selection
D)all possible regressions
E)backward selection

Question 54

Which of the following iterative search procedures for model building in a multiple regression analysis re-evaluates the contribution of variables previously included in the model after entering a new independent variable?

A)backward elimination
B)stepwise regression
C)forward selection
D)all possible regressions
E)backward selection

Question 55

Yvonne Lang, VP of Finance at Digital Components, Inc.(DCI), wants a regression model which predicts the average collection period on credit sales.Her data set includes two qualitative variables: sales discount rates (0%, 2%, 4%, and 6%), and total assets of credit customers (small, medium, and large).The number of dummy variables needed for "total assets of credit customer" in Yvonne's regression model is ___.

A)1
B)2
C)3
D)4
E)7

Question 56

If a qualitative variable has "c" categories, how many dummy variables must be created and used in the regression analysis?

A)c - 1
B)c
C)c + 1
D)c - 2
E)4 + c

Question 57

An "all possible regressions" search of a data set containing 7 independent variables will produce ___ regressions.

A)13
B)127
C)48
D)64
E)97

Question 58

After a transformation of the y-variable values into log y, and performing a regression analysis produced the following tables: For x₁= 10, the predicted value of y is ___.

A)155.79
B)1.25
C)2.42
D)189.06
E)18.90

Question 59

Abby Ross, a market specialist at the market research firm of Saez, Gann, and Spitz, is analyzing household budget data collected by her firm.Abby's dependent variable is monthly household expenditures on groceries (in $'s), and her independent variables are annual household income (in $1,000's)and household neighbourhood (0 = suburban, 1 = rural).Regression analysis of the data yielded the following table: Abby's model is ___.

A)y = 19.68247 + 10.01176 x₁ + 1.965934 x₂
B)y = 1.965934 + 9.940612 x₁ + 6.416667 x₂
C)y = 10.01176 + 0.174564 x₁ + 7.655776 x₂
D)y = 19.68247 - 1.735272 x₁ + 49.12456 x₂
E)y = 19.68247 + 1.735272 x₁ + 49.12456 x₂

Question 60

Abby Ross, a market specialist at the market research firm of Saez, Gann, and Spitz, is analyzing household budget data collected by her firm.Abby's dependent variable is monthly household expenditures on groceries (in $'s), and her independent variables are annual household income (in $1,000's)and household neighbourhood (0 = suburban, 1 = rural).Regression analysis of the data yielded the following table: For a suburban household with $70,000 annual income, Abby's model predicts monthly grocery expenditure of ___.

A)$141.15
B)$190.28
C)$164.52
D)$122.67
E)$241.15

Question 61

Inspection of the following table of correlation coefficients for variables in a multiple regression analysis reveals that the first independent variable that will be entered into the regression model by the forward selection procedure will be ___.

A)x₁
B)x₂
C)x₃
D)x₄
E)x₅

Question 62

A useful technique in controlling multicollinearity involves the ___.

A)use of variance inflation factors
B)use of the backward elimination procedure
C)use of the forward elimination procedure
D)use of the forward selection procedure
E)use of all possible regressions

Question 63

Carlos Martin, Director of Human Resources, is exploring employee absenteeism at the Plano Automotive Plant.A multiple regression analysis was performed using to the following variables.The results are presented below: Which of the following conclusions can be drawn from the above results?

A)All the independent variables in the regression are significant at 5% level.
B)Commuting distance is a highly significant (<1%)variable in explaining absenteeism.
C)Age of the employees tends to have a very significant (<1%)effect on absenteeism.
D)This model explains a little over 49% of the variability in absenteeism data.
E)A single-parent household employee is expected to be absent less number of days if all other variables are held constant compared to one who is not a single-parent household.

Question 64

Inspection of the following table of correlation coefficients for variables in a multiple regression analysis reveals potential multicollinearity with variables ___.

A)x₁ and x₅
B)x₂ and x₃
C)x₄ and x₂
D)x₄ and x₃
E)x₄ and y

Question 65

Large correlations between two or more independent variables in a multiple regression model could result in the problem of ___.

A)multicollinearity
B)autocorrelation
C)partial correlation
D)rank correlation
E)non-normality

Question 66

An "all possible regressions" search of a data set containing 4 independent variables will produce ___ regressions.

A)15
B)12
C)8
D)4
E)2

Question 67

An "all possible regressions" search of a data set containing "k" independent variables will produce ___ regressions.

A)2k -1
B)2^k-1
C)k² - 1
D)2^k - 1
E)2k

Question 68

An acceptable method of managing multicollinearity in a regression model is to ___.

A)use the forward selection procedure
B)use the backward elimination procedure
C)use the forward elimination procedure
D)use the stepwise regression procedure
E)use all possible regressions

Question 69

An "all possible regressions" search of a data set containing 9 independent variables will produce ___ regressions.

A)9
B)18
C)115
D)151
E)511

Question 70

Inspection of the following table of correlation coefficients for variables in a multiple regression analysis reveals potential multicollinearity with variables ___.

A)x₁ and x₂
B)x₁ and x₄
C)x₄ and x₅
D)x₄ and x₃
E)x₅ and y

Question 71

Inspection of the following table of correlation coefficients for variables in a multiple regression analysis reveals that the first independent variable that will be entered into the regression model by the forward selection procedure will be ___.

A)x₁
B)x₂
C)x₃
D)x₄
E)x₅

Question 72

An appropriate method to identify multicollinearity in a regression model is to ___.

A)examine a residual plot
B)examine the ANOVA table
C)examine a correlation matrix
D)examine the partial regression coefficients
E)examine the R² of the regression model

Question 73

Inspection of the following table of correlation coefficients for variables in a multiple regression analysis reveals that the first independent variable entered by the forward selection procedure will be ___.

A)x₁
B)x₂
C)x₃
D)x₄
E)x₅

Question 74

Inspection of the following table of correlation coefficients for variables in a multiple regression analysis reveals potential multicollinearity with variables ___.

A)x₁ and x₂
B)x₁ and x₅
C)x₃ and x₄
D)x₂ and x₅
E)x₃ and x₅

Question 75

Inspection of the following table of correlation coefficients for variables in a multiple regression analysis reveals that the first independent variable entered by the forward selection procedure will be ___.

A)x₂
B)x₃
C)x₄
D)x₅
E)x₁