Deck 14: Building Multiple Regression Models

Question 1

Qualitative data cannot be incorporated into linear regression models.

Answer 1

False

Question 2

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.

Answer 2

True

Question 3

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

Answer 3

False

Question 4

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

Question 5

The regression model y = $\beta$ ₀ + $\beta$ ₁ x₁ + $\beta$ ₂ x²₁ + $\varepsilon$ is called a quadratic model.

Question 6

Recognize when multicollinearity is present,understanding general techniques for preventing and controlling it.

Question 7

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.

Question 8

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 9

Use all possible regressions,stepwise regression,forward selection,and backward elimination search procedures to develop regression models that account for the most variation in the dependent variable and are parsimonious.

Question 10

Generalize linear regression models as polynomial regression models using model transformation and Tukey's ladder of transformation,accounting for possible interaction among the independent variables.

Question 11

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 12

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

Question 13

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

Question 14

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.

Question 15

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

Question 16

Examine the role of indicator,or dummy,variables as predictors or independent variables in multiple regression analysis.

Question 17

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.

Question 18

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 19

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

Question 20

Explain when to use logistic regression,and interpret its results.

Question 21

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

Question 22

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 23

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 24

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 25

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

Question 26

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 27

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 28

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 29

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 30

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 31

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

Question 32

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 33

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 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

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 36

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

Question 37

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

Question 38

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 39

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 40

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 41

Hope Hernandez,Marketing Manager of People's 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 42

Alan Bissell,a market analyst for City Sound Mart,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 43

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 44

Yvonne Yang,VP of Finance at Discrete 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 45

Alan Bissell,a market analyst for City Sound Mart,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

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 47

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 48

Alan Bissell,a market analyst for City Sound Mart,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 49

Abby Kratz,a market specialist at the market research firm of Saez,Sikes,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 50

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 51

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 52

Abby Kratz,a market specialist at the market research firm of Saez,Sikes,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 53

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 54

Hope Hernandez,Marketing Manager of People's 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 55

Abby Kratz,a market specialist at the market research firm of Saez,Sikes,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 56

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 57

Alan Bissell,a market analyst for City Sound Mart,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 58

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 59

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 60

Yvonne Yang,VP of Finance at Discrete 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 61

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 62

Carlos Cavazos,Director of Human Resources,is exploring employee absenteeism at the Plano Piano 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 63

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 64

Abby Kratz,a market specialist at the market research firm of Saez,Sikes,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 65

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 66

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 67

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 68

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 69

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

Question 70

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 71

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 72

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 73

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 74

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 75

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 76

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 77

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 78

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 79

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 80

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