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. \[\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\ \hline \text { Intercept } & 19.68247 & 10.01176 & 1.965934 & 0.077667 \\ \hline x _ { 1 } \text { (income) } & 1.735272 & 0.174564 & 9.940612 & 1.68 \mathrm { E } - 06 \\ \hline x _ { 2 } \text { (neighborhood) } & 49.12456 & 7.655776 & 6.416667 & 7.67 \mathrm { E } - 05 \\ \hline \end{array}\] For a rural household with ______ annual income, Abby's model predicts weekly grocery expenditure of $235.

A) $90,753.44 B) $92,257.51 C) $94,734.77 D) $95,773.44 E) $96,737.71 A) $90,753.44 B) $92,257.51 C) $94,734.77 D) $95,773.44 E) $96,737.71

Inspection of the following table of correlation coefficients for variables in a multiple regression analysis reveals potential multicollinearity with variables ___________. \[\begin{array} { | c | r | c | c | c | c | c | } \hline & y & x _ { 1 } & x _ { 2 } & x _ { 3 } & x _ { 4 } & x _ { 5 } \\ \hline y & 1 & & & & & \\ \hline x _ { 1 } & - 0.08301 & 1 & & & & \\ \hline x _ { 2 } & 0.236745 & - 0.51728 & 1 & & & \\ \hline x _ { 3 } & 0.155149 & - 0.22264 & - 0.00734 & 1 & & \\ \hline x _ { 4 } & 0.022234 & - 0.58079 & 0.884216 & 0.131956 & 1 & \\ \hline x _ { 5 } & 0.4808 & - 0.20467 & 0.078916 & 0.207477 & 0.103831 & 1 \\ \hline \end{array}\]

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

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. \[\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Standard Error } & t \text { Statistic } & p \text {-value } \\ \hline \text { Iritercept } & 1.7 & 0.384212 & 4.424638 & 0.00166 \\ \hline x _ { 1 } \text { (websitevisitors) } & 0.04 & 0.014029 & 2.851146 & 0.019054 \\ \hline x _ { 2 } \text { (download format) } & - 1.5666667 & 0.20518 & - 7.63558 & 3.21 E - 05 \\ \hline \end{array}\] For '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 A) $2,100,000 B) $524,507 C) $533,333 D) $729,683 E) $210,000

A multiple regression analysis produced the following tables. \[\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\ \hline \text { Irtercept } & 1411.876 & 7.621533 & & \\ \hline \boldsymbol { x } _ { 1 } & 35.18215 & 96.8433 & & \\ \hline \boldsymbol { x } _ { 1 } ^ { 2 } & - 7.721648 & \mathbf { 3 . 0 0 7 9 4 3 } & & \\ \hline \end{array}\] \[\begin{array} { | c | c | c | c | c | } \hline & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F \\ \hline \text { Regression } & 2 & 58567032 & 29283516 & 57.34861 \\ \hline \text { Residual } & 25 & 12765573 & 510622.9 & \\ \hline \text { Total } & 27 & 71332605 & & \\ \hline \end{array}\] If the predicted value of the dependent variable is 1000, then x1 = ______.

A) 4.50666 B) 8.158666 C) 9.928668 D) 10.15866 E) 11.928666 A) 4.50666 B) 8.158666 C) 9.928668 D) 10.15866 E) 11.928666

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$2 = 0, the critical t value is ____.

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

After a transformation of the y-variable values into log y, and performing a regression analysis produced the following tables. \[\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\ \hline \text { Iritercept } & 2.005349 & 0.097351 & 20.59923 & 4.81 \mathrm { E } - 18 \\ \hline \boldsymbol { x } & 0.027126 & 0.009518 & \mathbf { 2 . 8 4 9 8 4 3 } & \mathbf { 0 . 0 0 8 2 7 5 } \\ \hline \end{array}\] \[\begin{array} { | c | c | c | c | c | c | } \hline & \mathrm { df } & \text { SS } & \text { MS } & F & p \text {-value } \\ \hline \text { Regression } & 1 & 0.196642 & 0.196642 & 8.121607 & 0.008447 \\ \hline \text { Residual } & 26 & 0.629517 & 0.024212 & & \\ \hline \text { Total } & 27 & 0.826159 & & & \\ \hline \end{array}\] For x1= 10, the predicted value of y is ____________.

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

A research project was conducted to study the effect of a chemical on undesired insects.The researcher uses 6 dose levels, and at each level exposes 250 insects to the chemical and proceeds to count the number of insects that die.The researcher uses a binary logistic regression model to estimate the probability of death as a function of dose. Shown below is Minitab output from a logistic regression. \[\begin{array} { l c c c r r r } \text { Coefficients } \\ & & & & & \\ \text { Term } & \text { Coef } & \text { SE Coef } & 95 \% \text { CI } & \text { Z-Value } & \text { P-Value } & \text { VIF } \\ \text { Constant }& - 2.644 & 0.156 & ( - 2.950 , - 2.338 ) & - 16.94 & 0.000 & \\ \text { Dose } & 0.6740 & 0.0391 & ( 0.5973,0.7506 ) & 17.23 & 0.000 & 1.00 \\ & & & & \end{array}\] $\begin{array}{l} \text { Odd Ratios for Continuous Predictors } \\ \text { Odds Ratio } \quad \quad 95 \% \mathrm{CI} \\ \text { Dose } \quad 1.9621 \quad(1.8173,2.1184) \end{array}$ The predicted probability that an insect will die when exposed to the second dose is ____.

A) 0.1246 B) 0.1446 C) 0.1857 D) 0.2148 E) 0.2945 A) 0.1246 B) 0.1446 C) 0.1857 D) 0.2148 E) 0.2945

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. \[\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Standard Error } & t \text { Statistic } & p \text {-value } \\ \hline \text { Iritercept } & 1.7 & 0.384212 & 4.424638 & 0.00166 \\ \hline x _ { 1 } \text { (websitevisitors) } & 0.04 & 0.014029 & 2.851146 & 0.019054 \\ \hline x _ { 2 } \text { (download format) } & - 1.5666667 & 0.20518 & - 7.63558 & 3.21 E - 05 \\ \hline \end{array}\] For MP3 sales 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) $21,000,000 A) $2,100,000 B) $524,507 C) $533,333 D) $729,683 E) $21,000,000

Exam 14: Building Multiple Regression Models

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?

(Multiple Choice)

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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 the Minitab output from a logistic regression. Based on the results, the null hypothesis that all of the predictor variables are insignificant with coefficients of 0, should __________________.

(Multiple Choice)

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Question 62

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 For a rural household with ______ annual income, Abby's model predicts weekly grocery expenditure of $235.

(Multiple Choice)

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Question 63

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

(True/False)

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Question 64

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

(True/False)

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Question 65

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

(Multiple Choice)

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Question 66

Inspection of the following table of correlation coefficients for variables in a multiple regression analysis reveals potential multicollinearity with variables ___________. y y 1 -0.08301 1 0.236745 -0.51728 1 0.155149 -0.22264 -0.00734 1 0.022234 -0.58079 0.884216 0.131956 1 0.4808 -0.20467 0.078916 0.207477 0.103831 1

(Multiple Choice)

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Question 67

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?

(Multiple Choice)

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Question 68

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. Coefficients Standard Error t Statistic p -value Iritercept 1.7 0.384212 4.424638 0.00166 (websitevisitors) 0.04 0.014029 2.851146 0.019054 (download format) -1.5666667 0.20518 -7.63558 3.21E-05 For 'other' download formats with 10,000 website visitors, Alan's model predicts annual sales of heavy metal song downloads of ________________.

(Multiple Choice)

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Question 69

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

(True/False)

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Question 70

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 If the predicted value of the dependent variable is 1000, then x₁ = ______.

(Multiple Choice)

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Question 71

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: $\beta$ ₂ = 0, the critical t value is ____.

(Multiple Choice)

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Question 72

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

(True/False)

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Question 73

After a transformation of the y-variable values into log y, and performing a regression analysis produced the following tables. Coefficients Stardard Error t Statistic p -value Iritercept 2.005349 0.097351 20.59923 4.81-18 0.027126 0.009518 SS MS F p -value Regression 1 0.196642 0.196642 8.121607 0.008447 Residual 26 0.629517 0.024212 Total 27 0.826159 For x₁= 10, the predicted value of y is ____________.

(Multiple Choice)

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Question 74

A research project was conducted to study the effect of a chemical on undesired insects.The researcher uses 6 dose levels, and at each level exposes 250 insects to the chemical and proceeds to count the number of insects that die.The researcher uses a binary logistic regression model to estimate the probability of death as a function of dose. Shown below is Minitab output from a logistic regression. Coefficients Term Coef SE Coef 95\% CI Z-Value P-Value VIF Constant -2.644 0.156 (-2.950,-2.338) -16.94 0.000 Dose 0.6740 0.0391 (0.5973,0.7506) 17.23 0.000 1.00 Odd Ratios for Continuous Predictors Odds Ratio 95\% Dose 1.9621(1.8173,2.1184) The predicted probability that an insect will die when exposed to the second dose is ____.

(Multiple Choice)

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Question 75

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.

(True/False)

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Question 76

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. Coefficients Standard Error t Statistic p -value Iritercept 1.7 0.384212 4.424638 0.00166 (websitevisitors) 0.04 0.014029 2.851146 0.019054 (download format) -1.5666667 0.20518 -7.63558 3.21E-05 For MP3 sales with 10,000 website visitors, Alan's model predicts annual sales of heavy metal song downloads of ________________.

(Multiple Choice)

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Question 77

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. 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 Which of the individual predictors are found to be significant predictors of resting pulse rates at an alpha of 0.05?

(Multiple Choice)

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Question 78

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

(Multiple Choice)

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Question 79

To test the overall effectiveness of a logistic regression, a chi-squared statistic is used.

(True/False)

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Question 80

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?

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

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

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

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?

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

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

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.

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

To test the overall effectiveness of a logistic regression, a chi-squared statistic is used.

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

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?

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

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

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

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?

The regression model y = β\betaβ 0 + β\betaβ 1 x1 + β\betaβ 2 x21 + ε\varepsilonε is called a quadratic model.

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

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.

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

To test the overall effectiveness of a logistic regression, a chi-squared statistic is used.

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 different models.

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