Deck 14: Building Multiple Regression Models

Question 1

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.

Answer 1

True

Question 2

If each pair of independent variables is weakly correlated,there is no problem of multicollinearity.

Answer 2

False

Question 3

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

Answer 3

False

Question 4

If a square-transformation is applied to a series of positive numbers,all 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 5

Recoding data cannot improve the fit of a regression model.

Question 6

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

Question 7

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

Question 8

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

Question 9

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 10

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

Question 11

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

Question 12

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 13

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

Question 14

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

Question 15

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

Question 16

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

Question 17

Qualitative data can be incorporated into linear regression models using indicator variables.

Question 18

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 19

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

Question 20

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

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) an x² transform may be useful
D) no transform is needed
E) a (- x) transform may be useful

Question 22

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 23

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 24

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) 2,53.86
D) 262.19
E) 2,535.86

Question 25

A local parent group was concerned with the increasing school cost for families with school aged children.The parent group was interested in understanding the relationship between the
The academic grade level for the child and the total costs spent per child per academic year.They
Performed a multiple regression analysis using total cost as the dependent variable and academic
Year (x₁)as the independent variables.The 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 26

A local parent group was concerned with the increasing school cost for families with school aged children.The parent group was interested in understanding the relationship between the
The academic grade level for the child and the total costs spent per child per academic year.They
Performed a multiple regression analysis using total cost as the dependent variable and academic
Year (x₁)as the independent variables.The 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 27

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 28

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 29

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 30

The logistic regression model constrains the estimated probabilities to lie between 0 and 100.

Question 31

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 32

A local parent group was concerned with the increasing school cost for families with school aged children.The parent group was interested in understanding the relationship between the
The academic grade level for the child and the total costs spent per child per academic year.They
Performed a multiple regression analysis using total cost as the dependent variable and academic
Year (x₁)as the independent variables.The 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 33

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 34

A local parent group was concerned with the increasing school cost for families with school aged children.The parent group was interested in understanding the relationship between the
The academic grade level for the child and the total costs spent per child per academic year.They
Performed a multiple regression analysis using total cost as the dependent variable and academic
Year (x₁)as the independent variables.The 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 35

We may use logistic regression when the dependent variable is a dummy variable,coded 0 or 1.

Question 36

A local parent group was concerned with the increasing school cost for families with school aged children.The parent group was interested in understanding the relationship between the
The academic grade level for the child and the total costs spent per child per academic year.They
Performed a multiple regression analysis using total cost as the dependent variable and academic
Year (x₁)as the independent variables.The 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 37

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 38

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 39

If the variance inflation factor is bigger than 10,the regression analysis might suffer from the problem of multicollinearity.

Question 40

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 41

A local parent group was concerned with the increasing school cost for families with school aged children.The parent group was interested in understanding the relationship between the
The academic grade level for the child and the total costs spent per child per academic year.They
Performed a multiple regression analysis using total cost as the dependent variable and academic
Year (x₁)as the independent variables.The multiple regression analysis produced the following
Tables.
For a child in grade 5 (x₁= 2),the predicted value of y is ____________.

A) 707.91
B) 1,020.26
C) 781.99
D) 840.06
E) 1078.32

Question 42

A local parent group was concerned with the increasing school cost for families with school aged children.The parent group was interested in understanding the relationship between the
The academic grade level for the child and the total costs spent per child per academic year.They
Performed a multiple regression analysis using total cost as the dependent variable and academic
Year (x₁)as the independent variables.The multiple regression analysis produced the following
Tables.
For a child in grade 10 (x₁= 10)the predicted value of y is ____________.

A) 707.91
B) 1,117.38
C) 856.08
D) 2,189.54
E) 1,928.24

Question 43

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 weekly household expenditures on groceries (in $'s),and her independent variables are annual household income (in $1,000's)and household neighborhood (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 weekly expenditures for groceries
B) the suburban household's weekly expenditures for groceries will be $49 more
C) the rural household's weekly expenditures for groceries will be $49 more
D) the suburban household's weekly expenditures for groceries will be $8 more
E) the rural household's weekly expenditures for groceries will be $49 less

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 Online Mart,is analyzing sales from heavy metal song downloads.Alan's dependent variable is annual heavy metal song download sales (in $1,000,000's),and his independent variables are website visitors (in 1,000's)and type of download format requested (0 = MP3,1 = other).Regression analysis of the data yielded the following tables. For an MP3 sales with 10,000 website visitors,Alan's model predicts annual sales of heavy metal dong downloads of ________________.

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

Question 46

Hope Hernandez is the new regional Vice President for a large gasoline station chain.She wants a regression model to predict sales in the convenience stores. Her data set includes two qualitative variables: the gasoline station location (inner city,freeway,and suburbs),and curb appeal of the convenience store (low,medium,and high).The number of dummy variables needed for "curb appeal" in Hope's regression model is ______.

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

Question 47

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 weekly household expenditures on groceries (in $'s),and her independent variables are annual household income (in $1,000's)and household neighborhood (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 48

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 49

Which of the following iterative search procedures for model-building in a multiple regression analysis reevaluates the contribution of variables previously include 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 50

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 weekly household expenditures on groceries (in $'s),and her independent variables are annual household income (in $1,000's)and household neighborhood (0 = suburban,1 = rural). Regression analysis of the data yielded the following table. For a suburban household with $90,000 annual income,Abby's model predicts weekly grocery expenditure of ________________.

A) $156.19
B) $224.98
C) $444.62
D) $141.36
E) $175.86

Question 51

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 non-significant independent variables is a step-by-step manner?

A) Backward elimination
B) Stepwise regression
C) Forward selection
D) All possible regressions
E) Backward selection

Question 52

Alan Bissell,a market analyst for City Sound Online Mart,is analyzing sales from heavy metal song downloads.Alan's dependent variable is annual heavy metal song download sales (in $1,000,000's),and his independent variables are website visitors (in 1,000's)and type of download format requested (0 = MP3,1 = other).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 53

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 54

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 55

Alan Bissell,a market analyst for City Sound Online Mart,is analyzing sales from heavy metal song downloads.Alan's dependent variable is annual heavy metal song download sales (in $1,000,000's),and his independent variables are website visitors (in 1,000's)and type of download format requested (0 = MP3,1 = other).Regression analysis of the data yielded the following tables. For the same number of website visitors,what is difference between the predicted sales for MP3 versus 'other' heavy metal song downloads

A) $1,566,666 higher sales for 'other' formats
B) the same sales for both formats
C) $1,566,666 lower sales for the 'other' format
D) $1,700,000 higher sales for the MP3 format
E) $ 1,700,000 lower sales for the 'other' format

Question 56

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 weekly household expenditures on groceries (in $'s),and her independent variables are annual household income (in $1,000's)and household neighborhood (0 = suburban,1 = rural). Regression analysis of the data yielded the following table. For a rural household with $90,000 annual income,Abby's model predicts weekly grocery expenditure of ________________.

A) $156.19
B) $224.98
C) $444.62
D) $141.36
E) $175.86

Question 57

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 58

Alan Bissell,a market analyst for City Sound Online Mart,is analyzing sales from heavy metal song downloads.Alan's dependent variable is annual heavy metal song download sales (in $1,000,000's),and his independent variables are website visitors (in 1,000's)and type of download format requested (0 = MP3,1 = other).Regression analysis of the data yielded the following tables. For a 'other' download formats with 10,000 website visitors,Alan's model predicts annual sales of heavy metal song downloads of ________________.

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

Question 59

Hope Hernandez is the new regional Vice President for a large gasoline station chain.She wants a regression model to predict sales in the convenience stores. Her data set includes two qualitative variables: the gasoline station location (inner city,freeway,and suburbs),and curb appeal of the convenience store (low,medium,and high).The number of dummy variables needed for Hope's regression model is ______.

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

Question 60

A local parent group was concerned with the increasing school cost for families with school aged children.The parent group was interested in understanding the relationship between the
The academic grade level for the child and the total costs spent per child per academic year.They
Performed a multiple regression analysis using total cost as the dependent variable and academic
Year (x₁)as the independent variables.The 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 61

A research project was conducted to study the effect of smoking and weight upon resting pulse rate.The response variable is coded as 1 when the pulse rate is low and 0 when it high.Smoking is also coding as 1 when smoking and 0 when not smoking.Shown below is Minitab output from a logistic regression. Response Information
Variable Value Count
Rating Pulse 1 70 (Event)
0 22
Total 92
Logistic Regression Table
Odds 95% CI
Predictor Coef SE Coef Z P Ratio Lower Upper
Constant -1.98717 1.67930 -1.18 0.237
Weight 0.0250226 0.0122551 2.04 0.041 1.03 1.00 1.05
Smokes -1.19297 0.552980 -2.16 0.031 0.30 0.10 0.90
Log-Likelihood = -46.820
Test that all slopes are zero: G = 7.574,DF = 2,P-Value = 0.023
The log of the odds ratio or logit equation is:

A) log(S)=-1.19297+0.0250226 Weight-1.98717 Smokes
B) S=-1.98717+0.025226 Weight-1.19297 Smokes
C) Rating Pulse=-1.98717+0.025226 Weight-1.19297 Smokes
D) log(S) =-1.98717+0.025226 Weight-1.19297 Smokes
E) log(p)=-1.98717+0.025226 Weight-1.19297 Smokes

Question 62

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 63

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 64

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 65

Carlos Cavazos,Director of Human Resources,is exploring employee absenteeism at the Plano Piano Plant.A multiple regression analysis was performed using 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 all other variables held constant compared to one who is not a single-parent household.

Question 66

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 67

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 68

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 69

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 70

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

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 71

An "all possible regressions" search of a data set containing 8 independent variables will produce ______ regressions.

A) 8
B) 15
C) 256
D) 64
E) 255

Question 72

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 73

Suppose a company is interested in understanding the effect of age and gender on the likelihood a customer will purchase a new product.The data analyst intends to run a logistic regression on her data.Which of the following variable(s)will the analyst need to code as 0 or 1 prior to performing the logistic regression analysis?

A) age and gender
B) age and purchase status
C) age
D) purchase status
E) gender and purchase status

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

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 76

A multiple regression analysis produced the following tables. The minimum value of the predicted value of the dependent variable is reached when
X₁ = ______.

A) 2.15815
B) 3.18512
C) 3.37785
D) 3.40125
E) a value not listed here

Question 77

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 78

An "all possible regressions" search of a data set containing 5 independent variables will produce ______ regressions.

A) 31
B) 10
C) 25
D) 32
E) 24

Question 79

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

A) Backward elimination
B) Stepwise regression
C) Forward selection
D) All possible regressions
E) Forward elimination

Question 80

A useful technique in controlling multicollinearity involves the _________.

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