Question 1

Large correlations between two or more independent variables in a multiple regression model could result in the problem of ________.

Accepted Answer

A) multicollinearity 
B) autocorrelation 
C) partial correlation 
D) rank correlation 
E) non-normality 
A) multicollinearity 
B) autocorrelation 
C) partial correlation 
D) rank correlation 
E) non-normality A

Question 2

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 what annual income will a suburban household and a rural household have the same predicted weekly grocery spending?

Accepted Answer

A) $120,082.9 
B) $122,082.9 
C) $124,082.9 
D) The predicted weekly grocery spending of a rural household will always will be larger for a given annual income. 
E) The predicted weekly grocery spending of a suburban household will always will be larger for a given annual income. 
A) $120,082.9 
B) $122,082.9 
C) $124,082.9 
D) The predicted weekly grocery spending of a rural household will always will be larger for a given annual income. 
E) The predicted weekly grocery spending of a suburban household will always will be larger for a given annual income. D

Question 3

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

Accepted Answer

A) 2k -1 
B) 2k - 1 
C) k2 - 1 
D) 2k - 1 
E) 2k 
A) 2k -1 
B) 2k - 1 
C) k2 - 1 
D) 2k - 1 
E) 2k D

Question 4

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.

Accepted Answer

A) True 
 B)False

Question 5

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. $$\begin{array} { | c | c | c | c | c | } 
\hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \
\hline \text { Intercept } & 19.68247 & 10.01176 & 1.965934 & 0.077667 \
\hline x _ { 1 } \text { (income) } & 1.735272 & 0.174564 & 9.940612 & 1.68 \mathrm { E } - 06 \
\hline x _ { 2 } \text { (neighborhood) } & 49.12456 & 7.655776 & 6.416667 & 7.67 \mathrm { E } - 05 \
\hline
\end{array}$$ The marginal propensity to consume (MPC)is defined in economics as the proportion of an additional dollar of income that a household (or individual)consumes.Assume that grocery spending is the main expenditure of households.Then according to the regression analysis above, the MPC ______.

Accepted Answer

A) of rural households is equal to that of urban households, and this MPC decreases as households increase their annual income 
B) of rural households is larger than that of urban households, and both MPCs decrease as households increase their annual income 
C) of rural households is equal to that of urban households, and this MPC is constant as households increase their annual income 
D) of rural households is larger than that of urban households, and both MPCs are constant as households increase their annual income 
E) of rural households is larger than that of urban households, and both MPCs increase as households increase their annual income 
A) of rural households is equal to that of urban households, and this MPC decreases as households increase their annual income 
B) of rural households is larger than that of urban households, and both MPCs decrease as households increase their annual income 
C) of rural households is equal to that of urban households, and this MPC is constant as households increase their annual income 
D) of rural households is larger than that of urban households, and both MPCs are constant as households increase their annual income 
E) of rural households is larger than that of urban households, and both MPCs increase as households increase their annual income

Question 6

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 estimated odds of death at a given level divided by the estimated odds of death at the following level equals = ______.

Accepted Answer

A) 1.9621 
B) 0.6470 
C) 0.5097 
D) 0.3271 
E) 0.3008 
A) 1.9621 
B) 0.6470 
C) 0.5097 
D) 0.3271 
E) 0.3008

Question 7

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 $90,000 annual income, Abby's model predicts weekly grocery expenditure of ________________.

Accepted Answer

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

Question 8

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 ________.

Accepted Answer

A) 1 
B) 2 
C) 3 
D) 4 
E) 7 
A) 1 
B) 2 
C) 3 
D) 4 
E) 7

Question 9

A multiple regression analysis produced the following tables. $$\begin{array} { | c | c | c | c | c | } 
\hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \
\hline \text { Irtercept } & 1411.876 & 7.621533 & & \
\hline \boldsymbol { x } _ { 1 } & 35.18215 & 96.8433 & & \
\hline \boldsymbol { x } _ { 1 } ^ { 2 } & - 7.721648 & \mathbf { 3 . 0 0 7 9 4 3 } & & \
\hline
\end{array}$$ $$\begin{array} { | c | c | c | c | c | } 
\hline & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F \
\hline \text { Regression } & 2 & 58567032 & 29283516 & 57.34861 \
\hline \text { Residual } & 21 & 12765573 & 510622.9 & \
\hline \text { Total } & 23 & 71332605 & & \
\hline
\end{array}$$ Using $\alpha$= 0.01 to test the null hypothesis H0: $\beta$1 = $\beta$2 = 0, the critical F value is ______.

Accepted Answer

A) 8.09 
B) 6.89 
C) 6.09 
D) 5.78 
E) 5.09 
A) 8.09 
B) 6.89 
C) 6.09 
D) 5.78 
E) 5.09

Question 10

The following scatter plot indicates that _________.

Accepted Answer

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 
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 11

The following scatter plot indicates that _________.

Accepted Answer

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/y transform may be useful 
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/y transform may be useful

Question 12

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

Accepted Answer

A) True 
 B)False

Question 13

Inspection of the following table of correlation coefficients for variables in a multiple regression analysis reveals potential multicollinearity with variables ___________. $$\begin{array} { | c | r | c | r | c | c | r | } 
\hline & y & x _ { 1 } & x _ { 2 } & x _ { 3 } & x _ { 4 } & x _ { 5 } \
\hline y & 1 & & & & & \
\hline x _ { 1 } & - 0.0857 & 1 & & & & \
\hline x _ { 2 } & - 0.20246 & 0.868358 & 1 & & & \
\hline x _ { 3 } & - 0.22631 & - 0.10604 & - 0.14853 & 1 & & \
\hline x _ { 4 } & - 0.28175 & - 0.0685 & 0.41468 & - 0.14151 & 1 & \
\hline x _ { 5 } & 0.271105 & 0.150796 & 0.129388 & - 0.15243 & 0.00821 & 1 \
\hline
\end{array}$$

Accepted Answer

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

Question 14

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.

Accepted Answer

A) True 
 B)False

Question 15

If a coefficient of determination for a given model is 0.85, then its variance inflation factor is ______.

Accepted Answer

A) 8.5 
B) 7.7 
C) 6.2 
D) 4.9 
E) 6.7 
A) 8.5 
B) 7.7 
C) 6.2 
D) 4.9 
E) 6.7

Question 16

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. $$\begin{array} { | c | c | c | c | c | } 
\hline & \text { Coefficients } & \begin{array} { c } 
\text { Stardard } \
\text { Error }
\end{array} & \boldsymbol { t } \text { Statistic } & p \text {-value } \
\hline \text { Intercept } & 1.7 & 0.384212 & 4.424638 & 0.00166 \
\hline \boldsymbol { x } _ { 1 } \text { (website visitors) } & 0.04 & 0.014029 & \mathbf { 2 . 8 5 1 1 4 6 } & 0.019054 \
\hline \mathbf { x } _ { 2 } \text { (download fommat) } & - 1.5666667 & 0.20518 & - 7.63558 & \mathbf { 3 . 2 1 E - 0 5 } \
\hline
\end{array}$$ Alan's model is ________________.

Accepted Answer

A)   = 1.7 + 0.384212 x1 + 4.424638 x2 + 0.00166 x3 
B)   = 1.7 + 0.04 x1 + 1.5666667 x2 
C)   = 0.384212 + 0.014029 x1 + 0.20518 x2 
D)   = 4.424638 + 2.851146 x1 - 7.63558 x2 
E)   = 1.7 + 0.04 x1 - 1.5666667 x2 
A)   = 1.7 + 0.384212 x1 + 4.424638 x2 + 0.00166 x3 
B)   = 1.7 + 0.04 x1 + 1.5666667 x2 
C)   = 0.384212 + 0.014029 x1 + 0.20518 x2 
D)   = 4.424638 + 2.851146 x1 - 7.63558 x2 
E)   = 1.7 + 0.04 x1 - 1.5666667 x2

Question 17

If a qualitative variable has 4 categories, how many dummy variables must be created and used in the regression analysis?

Accepted Answer

A) 3 
B) 4 
C) 5 
D) 6 
E) 7 
A) 3 
B) 4 
C) 5 
D) 6 
E) 7

Question 18

Inspection of the following table of t values for variables in a multiple regression analysis reveals that the first independent variable entered by the forward selection procedure will be ___________. $$\begin{array} { | l | r | r | r | r | r | r | } 
\hline & y & x _ { 1 } & x _ { 2 } & x _ { 3 } & x _ { 4 } & x _ { 5 } \
\hline y & 1 & & & & & \
\hline x _ { 1 } & - 0.1661 & 1 & & & & \
\hline x _ { 2 } & 0.231849 & - 0.51728 & 1 & & & \
\hline x _ { 3 } & 0.423522 & - 0.22264 & - 0.00734 & 1 & & \
\hline x _ { 4 } & - 0.33227 & 0.028957 & - 0.49869 & 0.260586 & 1 & \
\hline x _ { 5 } & 0.199796 & - 0.20467 & 0.078916 & 0.207477 & 0.023839 & 1 \
\hline
\end{array}$$

Accepted Answer

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

Question 19

Inspection of the following table of t values for variables in a multiple regression analysis reveals that the first independent variable entered by the forward selection procedure will be ___________. $$\begin{array} { | c | c | c | c | c | c | c | } 
\hline & y & x _ { 1 } & x _ { 2 } & x _ { 3 } & x _ { 4 } & x _ { 5 } \
\hline y & 1 & & & & & \
\hline x _ { 1 } & - 0.44008 & 1 & & & & \
\hline x _ { 2 } & 0.566053 & - 0.51728 & 1 & & & \
\hline x _ { 3 } & 0.064919 & - 0.22264 & - 0.00734 & 1 & & \
\hline x _ { 4 } & - 0.35711 & 0.028957 & - 0.49869 & 0.260586 & 1 & \
\hline x _ { 5 } & 0.426363 & - 0.20467 & 0.078916 & 0.207477 & 0.023839 & 1 \
\hline
\end{array}$$

Accepted Answer

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

Question 20

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= 10, the predicted value of y is ____________.

Accepted Answer

A) 8.88. 
B) 2,031.38 
C) 2,53.86 
D) 262.19 
E) 2,535.86 
A) 8.88. 
B) 2,031.38 
C) 2,53.86 
D) 262.19 
E) 2,535.86

Large correlations between two or more independent variables in a multiple regression model could result in the problem of ________.

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

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.

The following scatter plot indicates that _________.

The following scatter plot indicates that _________.

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

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.

If a coefficient of determination for a given model is 0.85, then its variance inflation factor is ______.

If a qualitative variable has 4 categories, how many dummy variables must be created and used in the regression analysis?

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

Large correlations between two or more independent variables in a multiple regression model could result in the problem of ________.

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

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.

The following scatter plot indicates that _________.

The following scatter plot indicates that _________.

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

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.

If a coefficient of determination for a given model is 0.85, then its variance inflation factor is ______.

If a qualitative variable has 4 categories, how many dummy variables must be created and used in the regression analysis?

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