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. \[\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\ \hline \text { Intercept } & 19.68247 & 10.01176 & 1.965934 & 0.077667 \\ \hline x _ { 1 } \text { (income) } & 1.735272 & 0.174564 & 9.940612 & 1.68 \mathrm { E } - 06 \\ \hline x _ { 2 } \text { (neighborhood) } & 49.12456 & 7.655776 & 6.416667 & 7.67 \mathrm { E } - 05 \\ \hline \end{array}\] However, Abby has reasons to believe that actually suburban households have a higher propensity to spend in groceries than rural households, as they tend to make more impulse purchasing decisions.In this new model, the actual income coefficient for the suburban families is 1.735272$\alpha$, for some $\alpha$ > 1.If new data confirms that suburban houses with an annual income of $95,773.44 have the same weekly grocery spending as rural households, then $\alpha$ = ______.

A) 1.055587 B) 1.165587 C) 1.245587 D) 1.275587 E) 1.295587 A) 1.055587 B) 1.165587 C) 1.245587 D) 1.275587 E) 1.295587

A local parent group was concerned with the increasing cost of school for families with school aged children.The parent group was interested in understanding the relationship between 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. \[\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\ \hline \text { Intercept } & 707.9144 & 435.1183 & 1.626947 & 0.114567 \\ \hline \boldsymbol { x } _ { 1 } & 2.903307 & 81.62802 & 0.035568 & 0.971871 \\ \hline \mathbf { x } _ { 1 } ^ { 2 } & 11.91297 & 3.806211 & 3.129878 & 0.003967 \\ \hline \end{array}\] \[\begin{array} { | c | c | c | c | c | c | } \hline & \text { df } & \text { SS } & \text { MS } & F & p \text {-value } \\ \hline \text { Regression } & 2 & 32055153 & 16027577 & 47.34557 & 1.49 \mathrm { E } - 09 \\ \hline \text { Residual } & 27 & 9140128 & 338523.3 & & \\ \hline \text { Total } & 29 & 41195281 & & & \\ \hline \end{array}\] 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 A) ± 1.311 B) ± 1.699 C) ± 1.703 D) ± 2.502 E) ± 2.052

A multiple regression analysis produced the following tables. \[\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\ \hline \text { Irtercept } & 1411.876 & 762.1533 & 1.852483 & 0.074919 \\ \hline \boldsymbol { x } _ { 1 } & 35.18215 & 96.8433 & 0.363289 & 0.719218 \\ \hline \boldsymbol { x } _ { 1 } { } ^ { 2 } & 7.721648 & \mathbf { 3 . 0 0 7 9 4 3 } & 2.567086 & 0.016115\\ \hline \end{array}\] \[\begin{array} { | c | c | c | c | c | } \hline & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F \\ \hline \text { Regression } & 2 & 58567032 & 29283516 & 57.34861 \\ \hline \text { Residual } & 25 & 12765573 & 510622.9 & \\ \hline \text { Total } & 27 & 71332605 & & \\ \hline \end{array}\] 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 A) 5,204.18. B) 2,031.38 C) 2,538.86 D) 6262.19 E) 6,535.86

A multiple regression analysis produced the following tables. \[\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\ \hline & & & & \\ \hline \text { Irtercept } & 1411.876 & 762.1533 & 1.852483 & 0.074919 \\ \hline x _ { 1 } & 35.18215 & 96.8433 & 0.363289 & 0.719218 \\ \hline x _ { 1 } { } ^ { 2 } & 7.721648 & 3.007943 & 2.567086 & 0.016115 \\ \hline \end{array}\] \[\begin{array} { | c | c | c | c | c | } \hline & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F \\ \hline \text { Repression } & 2 & 58567032 & 29283516 & 57.34861 \\ \hline \text { Residual } & 25 & 12765573 & 5106229 & \\ \hline \text { Total } & 27 & 71332605 & & \\ \hline \end{array}\] 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 A) ± 1.316 B) ± 1.314 C) ± 1.703 D) ± 1.780 E) ± 1.708

A local parent group was concerned with the increasing cost of school for families with school aged children.The parent group was interested in understanding the relationship between 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. \[\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\ \hline \text { Intercept } & 707.9144 & 435.1183 & 1.626947 & 0.114567 \\ \hline \boldsymbol { x } _ { 1 } & 2.903307 & 81.62802 & 0.035568 & 0.971871 \\ \hline \mathbf { x } _ { 1 } { } ^ { 2 } & 11.91297 & 3.806211 & 3.129878 & 0.003967 \\ \hline \end{array}\] \[\begin{array} { | c | c | c | c | c | c | } \hline & \text { df } & \text { Ss } & \text { Ms } & F & p \text {-value } \\ \hline \text { Regression } & 2 & 32055153 & 16027577 & 47.34557 & 1.49 \mathrm { E } - 09 \\ \hline \text { Residual } & 27 & 9140128 & 338523.3 & & \\ \hline \text { Total } & 29 & 41195281 & & & \\ \hline \end{array}\] 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 A) 707.91 B) 1,117.38 C) 856.08 D) 2,189.54 E) 1,928.24

A local parent group was concerned with the increasing cost of school for families with school aged children.The parent group was interested in understanding the relationship between 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. \[\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\ \hline \text { Intercept } & 707.9144 & 435.1183 & 1.626947 & 0.114567 \\ \hline \boldsymbol { x } _ { 1 } & 2.903307 & 81.62802 & 0.035568 & 0.971871 \\ \hline \mathbf { x } _ { 1 } { } ^ { 2 } & 11.91297 & 3.806211 & 3.129878 & 0.003967 \\ \hline \end{array}\] \[\begin{array} { | c | c | c | c | c | c | } \hline & \text { Df } & \text { SS } & \text { MS } & F & p \text {-value } \\ \hline \text { Regression } & 2 & 32055153 & 16027577 & 47.34557 & 1.49 \mathrm { E } - 09 \\ \hline \text { Residual } & 27 & 9140128 & 338523.3 & & \\ \hline \text { Total } & 29 & 41195281 & & & \\ \hline \end{array}\] The regression equation for this analysis is ____________.

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

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. \[\begin{array} { | l | r | r | r | r | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\ \hline \text { Irtercept } & 19.68247 & 10.01176 & 1.965934 & 0.077667 \\ \hline x _ { 1 } \text { (incorne) } & 1.735272 & 0.174564 & 9.940612 & 1.68 \mathrm { E } - 06 \\ \hline x _ { 2 } \text { (neighborhood) } & 49.12456 & 7.655776 & 6.416667 & 7.67 \mathrm { E } - 05 \\ \hline \end{array}\] 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 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

A multiple regression analysis produced the following tables. \[\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\ \hline \text { Irtercept } & 1411.876 & 7.621533 & & \\ \hline \boldsymbol { x } _ { 1 } & 35.18215 & 96.8433 & & \\ \hline \boldsymbol { x } _ { 1 } ^ { 2 } & - 7.721648 & \mathbf { 3 . 0 0 7 9 4 3 } & & \\ \hline \end{array}\] \[\begin{array} { | c | c | c | c | c | } \hline & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F \\ \hline \text { Regression } & 2 & 58567032 & 29283516 & 57.34861 \\ \hline \text { Residual } & 25 & 12765573 & 510622.9 & \\ \hline \text { Total } & 27 & 71332605 & & \\ \hline \end{array}\] 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 A) 2.15815 B) 3.18512 C) 3.37785 D) 3.40125 E) a value not listed here

Inspection of the following table of correlation coefficients for variables in a multiple regression analysis reveals potential multicollinearity with variables ___________. \[\begin{array} { | c | c | c | c | c | c | c | } \hline & y & x _ { 1 } & x _ { 2 } & x _ { 3 } & x _ { 4 } & x _ { 5 } \\ \hline y & 1 & & & & & \\ \hline x _ { 1 } & 0.854168 & 1 & & & & \\ \hline x _ { 2 } & - 0.11828 & - 0.00383 & 1 & & & \\ \hline x _ { 3 } & - 0.12003 & - 0.08499 & - 0.14523 & 1 & & \\ \hline x _ { 4 } & 0.525901 & 0.118169 & - 0.14876 & 0.050042 & 1 & \\ \hline x _ { 5 } & - 0.18105 & - 0.07371 & 0.995886 & - 0.14151 & - 0.16934 & 1 \\ \hline \end{array}\]

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

Exam 14: Building Multiple Regression Models

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. Coefficients Stardard Error t Statistic p -value Intercept 19.68247 10.01176 1.965934 0.077667 (income) 1.735272 0.174564 9.940612 1.68-06 (neighborhood) 49.12456 7.655776 6.416667 7.67-05 However, Abby has reasons to believe that actually suburban households have a higher propensity to spend in groceries than rural households, as they tend to make more impulse purchasing decisions.In this new model, the actual income coefficient for the suburban families is 1.735272 $\alpha$ , for some $\alpha$ > 1.If new data confirms that suburban houses with an annual income of $95,773.44 have the same weekly grocery spending as rural households, then $\alpha$ = ______.

(Multiple Choice)

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Question 41

The following scatter plot indicates that _________.

(Multiple Choice)

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Question 42

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.

(True/False)

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Question 43

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?

(Multiple Choice)

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Question 44

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 the Minitab output from a logistic regression. The log of the odds ratio or logit equation is:

(Multiple Choice)

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Question 45

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

(Multiple Choice)

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Question 46

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

(True/False)

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Question 47

A local parent group was concerned with the increasing cost of school for families with school aged children.The parent group was interested in understanding the relationship between 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. Coefficients Stardard Error t Statistic p -value Intercept 707.9144 435.1183 1.626947 0.114567 2.903307 81.62802 0.035568 0.971871 11.91297 3.806211 3.129878 0.003967 df SS MS F p -value Regression 2 32055153 16027577 47.34557 1.49-09 Residual 27 9140128 338523.3 Total 29 41195281 Using $\alpha$ = 0.05 to test the null hypothesis H₀: $\beta$ ₁ = 0, the critical t value is ____.

(Multiple Choice)

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Question 48

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 ______.

(Multiple Choice)

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Question 49

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

(True/False)

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Question 50

A multiple regression analysis produced the following tables. Coefficients Stardard Error t Statistic p -value Irtercept 1411.876 762.1533 1.852483 0.074919 35.18215 96.8433 0.363289 0.719218 7.721648 2.567086 0.016115 F Regression 2 58567032 29283516 57.34861 Residual 25 12765573 510622.9 Total 27 71332605 For x₁= 20, the predicted value of y is ____________.

(Multiple Choice)

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Question 51

A multiple regression analysis produced the following tables. Coefficients Stardard Error t Statistic p -value Irtercept 1411.876 762.1533 1.852483 0.074919 35.18215 96.8433 0.363289 0.719218 7.721648 3.007943 2.567086 0.016115 F Repression 2 58567032 29283516 57.34861 Residual 25 12765573 5106229 Total 27 71332605 Using $\alpha$ = 0.10 to test the null hypothesis H₀: $\beta$ ₂ = 0, the critical t value is ____.

(Multiple Choice)

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Question 52

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

(Multiple Choice)

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Question 53

A local parent group was concerned with the increasing cost of school for families with school aged children.The parent group was interested in understanding the relationship between 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. Coefficients Stardard Error t Statistic p -value Intercept 707.9144 435.1183 1.626947 0.114567 2.903307 81.62802 0.035568 0.971871 11.91297 3.806211 3.129878 0.003967 df Ss Ms F p -value Regression 2 32055153 16027577 47.34557 1.49-09 Residual 27 9140128 338523.3 Total 29 41195281 For a child in grade 10 (x₁= 10)the predicted value of y is ____________.

(Multiple Choice)

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Question 54

Which of the following problems is not caused by multicollinearity?

(Multiple Choice)

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Question 55

A local parent group was concerned with the increasing cost of school for families with school aged children.The parent group was interested in understanding the relationship between 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. Coefficients Stardard Error t Statistic p -value Intercept 707.9144 435.1183 1.626947 0.114567 2.903307 81.62802 0.035568 0.971871 11.91297 3.806211 3.129878 0.003967 Df SS MS F p -value Regression 2 32055153 16027577 47.34557 1.49-09 Residual 27 9140128 338523.3 Total 29 41195281 The regression equation for this analysis is ____________.

(Multiple Choice)

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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. Coefficients Stardard Error t Statistic p -value Irtercept 19.68247 10.01176 1.965934 0.077667 (incorne) 1.735272 0.174564 9.940612 1.68-06 (neighborhood) 49.12456 7.655776 6.416667 7.67-05 For two households, one suburban and one rural, Abby's model predicts ________.

(Multiple Choice)

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Question 57

A multiple regression analysis produced the following tables. Coefficients Stardard Error t Statistic p -value Irtercept 1411.876 7.621533 35.18215 96.8433 -7.721648 F Regression 2 58567032 29283516 57.34861 Residual 25 12765573 510622.9 Total 27 71332605 The minimum value of the predicted value of the dependent variable is reached when X₁ = ______.

(Multiple Choice)

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Question 58

Inspection of the following table of correlation coefficients for variables in a multiple regression analysis reveals potential multicollinearity with variables ___________. y y 1 0.854168 1 -0.11828 -0.00383 1 -0.12003 -0.08499 -0.14523 1 0.525901 0.118169 -0.14876 0.050042 1 -0.18105 -0.07371 0.995886 -0.14151 -0.16934 1

(Multiple Choice)

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Question 59

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

(Multiple Choice)

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Question 60

The following scatter plot indicates that _________.

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.

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?

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

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

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

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

Which of the following problems is not caused by multicollinearity?

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

Introduction to Statistics and Business Analytics

Visualizing Data With Charts and Graphs

Descriptive Statistics

Probability

Discrete Distributions

Continuous Distributions

Sampling and Sampling Distributions

Statistical Inference: Estimation for Single Populations

Statistical Inference: Hypothesis Testing for Single Populations

Statistical Inferences About Two Populations

Analysis of Variance and Design of Experiments

Simple Regression Analysis and Correlation

Multiple Regression Analysis

Time-Series Forecasting and Index Numbers

Analysis of Categorical Data

Nonparametric Statistics

Statistical Quality Control

Decision Analysis

Filters

Exam 14: Building Multiple Regression Models

The following scatter plot indicates that _________.

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.

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?

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

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

The regression model y = β\betaβ 0 + β\betaβ 1 x1 + β\betaβ 2 x2 + β\betaβ 3 x3 + ε\varepsilonε is a third order model.

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

Which of the following problems is not caused by multicollinearity?

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

Introduction to Statistics and Business Analytics

Visualizing Data With Charts and Graphs

Descriptive Statistics

Probability

Discrete Distributions

Continuous Distributions

Sampling and Sampling Distributions

Statistical Inference: Estimation for Single Populations

Statistical Inference: Hypothesis Testing for Single Populations

Statistical Inferences About Two Populations

Analysis of Variance and Design of Experiments

Simple Regression Analysis and Correlation

Multiple Regression Analysis

Time-Series Forecasting and Index Numbers

Analysis of Categorical Data

Nonparametric Statistics

Statistical Quality Control

Decision Analysis

Filters

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

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