A multiple regression analysis produced the following tables. \[\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\ \hline & & & & \\ \hline \text { Irtercept } & 1411.876 & 762.1533 & 1.852483 & 0.074919 \\ \hline x _ { 1 } & 35.18215 & 96.8433 & 0.363289 & 0.719218 \\ \hline x _ { 1 } { } ^ { 2 } & 7.721648 & 3.007943 & 2.567086 & 0.016115 \\ \hline \end{array}\] \[\begin{array} { | c | c | c | c | c | } \hline & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F \\ \hline \text { Repression } & 2 & 58567032 & 29283516 & 57.34861 \\ \hline \text { Residual } & 25 & 12765573 & 5106229 & \\ \hline \text { Total } & 27 & 71332605 & & \\ \hline \end{array}\] The sample size for this analysis is ____________.

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

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. \[\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\ \hline \text { Intercept } & 707.9144 & 435.1183 & 1.626947 & 0.114567 \\ \hline \boldsymbol { x } _ { 1 } & 2.903307 & 81.62802 & 0.035568 & 0.971871 \\ \hline \mathbf { x } _ { 1 } { } ^ { 2 } & 11.91297 & 3.806211 & 3.129878 & 0.003967 \\ \hline \end{array}\] \[\begin{array} { | c | c | c | c | c | c | } \hline & \mathrm { df } & \mathbf { 5 s } & \mathrm { MS } & F & p \text {-value } \\ \hline \text { Regression } & 2 & 32055153 & 16027577 & 47.34557 & 1.49 \mathrm { E } - 09 \\ \hline \text { Residual } & 27 & 9140128 & 338523.3 & & \\ \hline \text { Total } & \mathbf { 2 9 } & 41195281 & & & \\ \hline \end{array}\] 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 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

A multiple regression analysis produced the following tables. \[\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\ \hline & & & & \\ \hline \text { Irtercept } & 1411.876 & 762.1533 & 1.852483 & 0.074919 \\ \hline x _ { 1 } & 35.18215 & 96.8433 & 0.363289 & 0.719218 \\ \hline x _ { 1 } { } ^ { 2 } & 7.721648 & 3.007943 & 2.567086 & 0.016115 \\ \hline \end{array}\] \[\begin{array} { | c | c | c | c | c | } \hline & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F \\ \hline \text { Regression } & 2 & 58567032 & 29283516 & 57.34861 \\ \hline \text { Residual } & 25 & 12765573 & 510622.9 & \\ \hline \text { Total } & 27 & 71332605 & & \\ \hline \end{array}\] 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 A) 4.24 B) 3.39 C) 5.57 D) 3.35 E) 2.35

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. \[\begin{array} { | c | c | c | c | c | } \hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \\ \hline \text { Intercept } & 707.9144 & 435.1183 & 1.626947 & 0.114567 \\ \hline \boldsymbol { x } _ { 1 } & 2.903307 & 81.62802 & 0.035568 & 0.971871 \\ \hline \mathbf { x } _ { 1 } { } ^ { 2 } & 11.91297 & 3.806211 & 3.129878 & 0.003967 \\ \hline \end{array}\] \[\begin{array} { | c | c | c | c | c | c | } \hline & \mathrm { df } & \mathbf { 5 s } & \mathrm { MS } & F & p \text {-value } \\ \hline \text { Regression } & 2 & 32055153 & 16027577 & 47.34557 & 1.49 \mathrm { E } - 09 \\ \hline \text { Residual } & 27 & 9140128 & 338523.3 & & \\ \hline \text { Total } & \mathbf { 2 9 } & 41195281 & & & \\ \hline \end{array}\] 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 A) 5.42 B) 5.49 C) 7.60 D) 3.35 E) 2.49

Inspection of the following table of t values 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 ___________. \[\begin{array} { | c | r | c | r | c | c | r | } \hline & y & x _ { 1 } & x _ { 2 } & x _ { 3 } & x _ { 4 } & x _ { 5 } \\ \hline y & 1 & & & & & \\ \hline x _ { 1 } & - 0.0857 & 1 & & & & \\ \hline x _ { 2 } & - 0.20246 & 0.868358 & 1 & & & \\ \hline x _ { 3 } & - 0.22631 & - 0.10604 & - 0.14853 & 1 & & \\ \hline x _ { 4 } & - 0.28175 & - 0.0685 & 0.41468 & - 0.14151 & 1 & \\ \hline x _ { 5 } & 0.271105 & 0.150796 & 0.129388 & - 0.15243 & 0.00821 & 1 \\ \hline \end{array}\]

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

Exam 14: Building Multiple Regression Models

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 ______.

(Multiple Choice)

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Question 81

Suppose a company is interested in understanding the effect of age and sex 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?

(Multiple Choice)

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Question 82

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

(True/False)

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Question 83

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 The sample size for this analysis is ____________.

(Multiple Choice)

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Question 84

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 F p -value Regression 2 32055153 16027577 47.34557 1.49-09 Residual 27 9140128 338523.3 Total 41195281 These results indicate that ____________.

(Multiple Choice)

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Question 85

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 Regression 2 58567032 29283516 57.34861 Residual 25 12765573 510622.9 Total 27 71332605 Using $\alpha$ = 0.05 to test the null hypothesis H₀: $\beta$ ₁ = $\beta$ ₂ = 0, the critical F value is ____.

(Multiple Choice)

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Question 86

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 F p -value Regression 2 32055153 16027577 47.34557 1.49-09 Residual 27 9140128 338523.3 Total 41195281 Using $\alpha$ = 0.01 to test the null hypothesis H₀: $\beta$ ₁ = $\beta$ ₂ = 0, the critical F value is ____.

(Multiple Choice)

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Question 87

Inspection of the following table of t values 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 ___________. y y 1 -0.0857 1 -0.20246 0.868358 1 -0.22631 -0.10604 -0.14853 1 -0.28175 -0.0685 0.41468 -0.14151 1 0.271105 0.150796 0.129388 -0.15243 0.00821 1

(Multiple Choice)

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Question 88

When structuring a logistic regression model, only one independent or predictor variable can be used.

(True/False)

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Question 89

If there are 6 independent variables, then there are possible regressions with 2 predictors and possible regressions with 3 predictors.

(Multiple Choice)

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Question 90

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

(True/False)

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Question 91

A regression analysis conducted to predict an independent variable by other independent variables ______.

(Multiple Choice)

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Question 92

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.

(True/False)

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Question 93

A researcher wants to address multicollinearity using the guideline that a variance inflation factor (VIF)greater than 9 will indicate a severe multicollinearity problem.This means that the highest coefficient of determination allowed will be ______.

(Multiple Choice)

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Question 94

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 ________.

(Multiple Choice)

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Question 95

Recoding data cannot improve the fit of a regression model.

(True/False)

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Question 96

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

(True/False)

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Question 97

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. $\begin{array}{c}\begin{array}{|l|}\hline \text { } \\\hline \text {Intercept}\\\hline \text { X_{1} (income)}\\\hline \text {$ \mathrm{X}_{2} $}\\ \text {(neighborhood)}\\\hline \end{array}\begin{array}{l}\hline \text { Coefficients }\\\hline 19.68247 \\\hline 1.735272 \\\hline 49.12456\\\\\hline \end{array}\begin{array}{|l|}\hline \text {Standard Error}\\\hline10.01176 \\\hline 0.174564 \\\hline 7.655776\\\\\hline \end{array}\begin{array}{l|}\hline t \text { Statistic } \\\hline 1.965934 \\\hline 9.940612 \\\hline 6.416667 \\\\\hline \end{array}\begin{array}{l|}\hline p \text {-value }\\\hline0.077667\\\hline1.68 \mathrm{E}-06\\\hline7.67 \mathrm{E}-05\\\\\hline\end{array}\end{array}$ Abby's model is ________________.

(Multiple Choice)

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Question 98

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

(True/False)

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Question 99

The following scatter plot indicates that _________.

(Multiple Choice)

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Question 100

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

When structuring a logistic regression model, only one independent or predictor variable can be used.

If there are 6 independent variables, then there are possible regressions with 2 predictors and possible regressions with 3 predictors.

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

A regression analysis conducted to predict an independent variable by other independent variables ______.

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.

A researcher wants to address multicollinearity using the guideline that a variance inflation factor (VIF)greater than 9 will indicate a severe multicollinearity problem.This means that the highest coefficient of determination allowed will be ______.

Recoding data cannot improve the fit of a regression model.

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

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

The following scatter plot indicates that _________.

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

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

When structuring a logistic regression model, only one independent or predictor variable can be used.

If there are 6 independent variables, then there are ______ possible regressions with 2 predictors and ______ possible regressions with 3 predictors.

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

A regression analysis conducted to predict an independent variable by other independent variables ______.

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.

A researcher wants to address multicollinearity using the guideline that a variance inflation factor (VIF)greater than 9 will indicate a severe multicollinearity problem.This means that the highest coefficient of determination allowed will be ______.

Recoding data cannot improve the fit of a regression model.

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

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

The following scatter plot indicates that _________.

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 there are 6 independent variables, then there are possible regressions with 2 predictors and possible regressions with 3 predictors.