Question 1

In a multiple regression model, the error term $\varepsilon$ is assumed to be a random variable with a mean of

Accepted Answer

A) zero 
B) -1 
C) 1 
D) any value 
A) zero 
B) -1 
C) 1 
D) any value A

Question 2

The following regression model has been proposed to predict sales at a furniture store.   = 10 - 4x1 + 7x2 + 18x3
where
x1 = competitor's previous day's sales (in $1,000s)
x2 = population within 1 mile (in 1000s)
x3 = 1 if any form of advertising was used, 0 if otherwise   = sales (in $1,000s) 
a.Fully interpret the meaning of the coefficient of x3.
b.Predict sales (in dollars) for a store with competitor's previous day's sale of $3,000, a population of 10,000 within 1 mile, and six radio advertisements.

Accepted Answer

a.When advertising was used, sales were higher by $18,000.b.$86,000

Question 3

A variable that cannot be measured in terms of how much or how many but instead is assigned values to represent categories is called

Accepted Answer

A) an interaction 
B) a constant variable 
C) a category variable 
D) a qualitative variable 
A) an interaction 
B) a constant variable 
C) a category variable 
D) a qualitative variable D

Question 4

In regression analysis, the response variable is the

Accepted Answer

A) independent variable 
B) dependent variable 
C) slope of the regression function 
D) intercept 
A) independent variable 
B) dependent variable 
C) slope of the regression function 
D) intercept

Question 5

In multiple regression analysis, the correlation among the independent variables is termed

Accepted Answer

A) homoscedasticity 
B) linearity 
C) multicollinearity 
D) adjusted coefficient of determination 
A) homoscedasticity 
B) linearity 
C) multicollinearity 
D) adjusted coefficient of determination

Question 6

Exhibit 15-5
Below you are given a partial Excel output based on a sample of 25 observations.  
-Refer to Exhibit 15-5. The estimated regression equation is

Accepted Answer

A) y = $\beta$0 + $\beta$1x1 + $\beta$2x2 + $\beta$3x3 + $\varepsilon$ 
B) E(y) = $\beta$0 + $\beta$1x1 + $\beta$2x2 + $\beta$3x3 
C) = 145.321 + 25.625x1 - 5.720x2 + 0.823x3 
D) = 48.682 + 9.15x1 + 3.575x2 + 0.183x3 
A) y = $\beta$0 + $\beta$1x1 + $\beta$2x2 + $\beta$3x3 + $\varepsilon$ 
B) E(y) = $\beta$0 + $\beta$1x1 + $\beta$2x2 + $\beta$3x3 
C) = 145.321 + 25.625x1 - 5.720x2 + 0.823x3 
D) = 48.682 + 9.15x1 + 3.575x2 + 0.183x3

Question 7

Shown below is a partial Excel output from a regression analysis.   
a.Use the above results and write the regression equation.
b.Compute the coefficient of determination and fully interpret its meaning.
c.Is the regression model significant? Perform an F test and let $\alpha$ = 0.05.
d.At $\alpha$ = 0.05, test to see if there is a relation between x1 and y.
e.At $\alpha$ = 0.05, test to see if there is a relation between x3 and y.

Accepted Answer

a.= 10 - 2x₁ + 6x₂

Question 8

The adjusted multiple coefficient of determination is adjusted for

Accepted Answer

A) the number of dependent variables 
B) the number of independent variables 
C) the number of equations 
D) detrimental situations 
A) the number of dependent variables 
B) the number of independent variables 
C) the number of equations 
D) detrimental situations

Question 9

Exhibit 15-5
Below you are given a partial Excel output based on a sample of 25 observations.  
-Refer to Exhibit 15-5. Carry out the test of significance for the parameter $\beta$1 at the 5% level. The null hypothesis should be

Accepted Answer

A) rejected 
B) not rejected 
C) revised 
D) None of these alternatives is correct. 
A) rejected 
B) not rejected 
C) revised 
D) None of these alternatives is correct.

Question 10

Below you are given a partial ANOVA table based on a sample of 12 observations relating the number of personal computers sold by a computer shop per month (y), unit price (x1 in $1,000) and the number of advertising spots (x2) they used on a local television station.   
a.At $\alpha$ = 0.05 level of significance, test to determine if the model is significant. That is, determine if there exists a significant relationship between the independent variables and the dependent variable.
b.Determine the multiple coefficient of determination.
c.Determine the adjusted multiple coefficient of determination.

Accepted Answer

a.F = 16.133 > 4.26;

Question 11

Exhibit 15-8
The following estimated regression model was developed relating yearly income (y in $1,000s) of 30 individuals with their age (xS1U1B11S1U1B0) and their gender (xS1U1B12S1U1B0) (0 if male and 1 if female).   = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0
Also provided are SST = 1,200 and SSE = 384.
-A regression model involved 18 independent variables and 200 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

Accepted Answer

A) 18 degrees of freedom 
B) 200 degrees of freedom 
C) 199 degrees of freedom 
D) 181 degrees of freedom 
A) 18 degrees of freedom 
B) 200 degrees of freedom 
C) 199 degrees of freedom 
D) 181 degrees of freedom

Question 12

As the goodness of fit for the estimated multiple regression equation increases,

Accepted Answer

A) the value of the adjusted multiple coefficient of determination decreases 
B) the value of the regression equation's constant b0 decreases 
C) the value of the multiple coefficient of determination increases 
D) the value of the correlation coefficient increases 
A) the value of the adjusted multiple coefficient of determination decreases 
B) the value of the regression equation's constant b0 decreases 
C) the value of the multiple coefficient of determination increases 
D) the value of the correlation coefficient increases

Question 13

In a multiple regression model, the variance of the error term $\varepsilon$ is assumed to be

Accepted Answer

A) the same for all values of the dependent variable 
B) zero 
C) the same for all values of the independent variable 
D) -1 
A) the same for all values of the dependent variable 
B) zero 
C) the same for all values of the independent variable 
D) -1

Question 14

The following regression model has been proposed to predict sales at a fast food outlet.   = 18 - 2x1 + 7x2 + 15x3
where
x1 = the number of competitors within 1 mile
x2 = the population within 1 mile (in 1,000s)
x3 = 1 if drive-up windows are present, 0 otherwise   = sales (in $1,000s) 
a.What is the interpretation of 15 (the coefficient of x3) in the regression equation?
b.Predict sales for a store with 2 competitors, a population of 10,000 within one mile, and one drive-up window (give the answer in dollars).
c.Predict sales for the store with 2 competitors, a population of 10,000 within one mile, and no drive-up window (give the answer in dollars).

Accepted Answer

a.Sales of stores with drive-u

Question 15

Exhibit 15-8
The following estimated regression model was developed relating yearly income (y in $1,000s) of 30 individuals with their age (xS1U1B11S1U1B0) and their gender (xS1U1B12S1U1B0) (0 if male and 1 if female).   = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0
Also provided are SST = 1,200 and SSE = 384.
-The least squares criterion is

Accepted Answer

A)  min   
B)  min   
C)  min   
D)  min   
A)  min   
B)  min   
C)  min   
D)  min

Question 16

Exhibit 15-8
The following estimated regression model was developed relating yearly income (y in $1,000s) of 30 individuals with their age (xS1U1B11S1U1B0) and their gender (xS1U1B12S1U1B0) (0 if male and 1 if female).   = 30 + 0.7xS1U1B11S1U1B0 + 3xS1U1B12S1U1B0
Also provided are SST = 1,200 and SSE = 384.
-The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the

Accepted Answer

A) standard error 
B) residual 
C) predicted interval 
D) variance 
A) standard error 
B) residual 
C) predicted interval 
D) variance

Question 17

Exhibit 15-7
A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares.SSR = 165
SSE = 60
-Refer to Exhibit 15-7. The test statistic from the information provided is

Accepted Answer

A) 2.110 
B) 3.480 
C) 4.710 
D) 6.875 
A) 2.110 
B) 3.480 
C) 4.710 
D) 6.875

Question 18

Exhibit 15-6
Below you are given a partial Excel output based on a sample of 16 observations.  
-A multiple regression model has the form   = 5 + 6x + 7w As x increases by 1 unit (holding w constant), y is expected to

Accepted Answer

A) increase by 11 units 
B) decrease by 11 units 
C) increase by 6 units 
D) decrease by 6 units 
A) increase by 11 units 
B) decrease by 11 units 
C) increase by 6 units 
D) decrease by 6 units

Question 19

Exhibit 15-5
Below you are given a partial Excel output based on a sample of 25 observations.  
-Refer to Exhibit 15-5. The interpretation of the coefficient on x1 is that

Accepted Answer

A) a one unit change in x1 will lead to a 25.625 unit change in y 
B) a one unit change in x1 will lead to a 25.625 unit increase in y when all other variables are held constant 
C) a one unit change in x1 will lead to a 25.625 unit increase in x2 when all other variables are held constant 
D) It is impossible to interpret the coefficient. 
A) a one unit change in x1 will lead to a 25.625 unit change in y 
B) a one unit change in x1 will lead to a 25.625 unit increase in y when all other variables are held constant 
C) a one unit change in x1 will lead to a 25.625 unit increase in x2 when all other variables are held constant 
D) It is impossible to interpret the coefficient.

Question 20

Exhibit 15-2
A regression model between sales (y in $1,000), unit price (xS1U1B11S1U1B0 in dollars) and television advertisement (xS1U1B12S1U1B0 in dollars) resulted in the following function:   = 7 - 3xS1U1B11S1U1B0 + 5xS1U1B12S1U1B0
For this model SSR = 3500, SSE = 1500, and the sample size is 18.
-Refer to Exhibit 15-2. The coefficient of the unit price indicates that if the unit price is

Accepted Answer

A) increased by $1 (holding advertising constant), sales are expected to increase by $3 
B) decreased by $1 (holding advertising constant), sales are expected to decrease by $3 
C) increased by $1 (holding advertising constant), sales are expected to increase by $4,000 
D) increased by $1 (holding advertising constant), sales are expected to decrease by $3,000 
A) increased by $1 (holding advertising constant), sales are expected to increase by $3 
B) decreased by $1 (holding advertising constant), sales are expected to decrease by $3 
C) increased by $1 (holding advertising constant), sales are expected to increase by $4,000 
D) increased by $1 (holding advertising constant), sales are expected to decrease by $3,000

In a multiple regression model, the error term $\varepsilon$ is assumed to be a random variable with a mean of

A variable that cannot be measured in terms of how much or how many but instead is assigned values to represent categories is called

In regression analysis, the response variable is the

In multiple regression analysis, the correlation among the independent variables is termed

Exhibit 15-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 15-5. The estimated regression equation is

The adjusted multiple coefficient of determination is adjusted for

As the goodness of fit for the estimated multiple regression equation increases,

In a multiple regression model, the variance of the error term $\varepsilon$ is assumed to be

Exhibit 15-8 The following estimated regression model was developed relating yearly income (y in $1,000s) of 30 individuals with their age (x₁) and their gender (x₂) (0 if male and 1 if female). = 30 + 0.7x₁ + 3x₂ Also provided are SST = 1,200 and SSE = 384. -The least squares criterion is

Exhibit 15-7 A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares.SSR = 165 SSE = 60 -Refer to Exhibit 15-7. The test statistic from the information provided is

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -A multiple regression model has the form = 5 + 6x + 7w As x increases by 1 unit (holding w constant), y is expected to

Exhibit 15-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 15-5. The interpretation of the coefficient on x₁ is that

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Inference About Means and Proportions With Two Populations

Inferences About Population Variances

Tests of Goodness of Fit, Independence and Multiple Proportions

Experimental Design and Analysis of Variance

Simple Linear Regression

Regression Analysis: Model Building

Time Series Analysis and Forecasting

Nonparametric Methods

Statistical Methods for Quality Control

Decision Analysis

Sample Survey

Filters

Exam 15: Multiple Regression

In a multiple regression model, the error term ε\varepsilonε is assumed to be a random variable with a mean of

A variable that cannot be measured in terms of how much or how many but instead is assigned values to represent categories is called

In regression analysis, the response variable is the

In multiple regression analysis, the correlation among the independent variables is termed

Exhibit 15-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 15-5. The estimated regression equation is

The adjusted multiple coefficient of determination is adjusted for

Exhibit 15-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 15-5. Carry out the test of significance for the parameter β\betaβ 1 at the 5% level. The null hypothesis should be

As the goodness of fit for the estimated multiple regression equation increases,

In a multiple regression model, the variance of the error term ε\varepsilonε is assumed to be

Exhibit 15-8 The following estimated regression model was developed relating yearly income (y in $1,000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female). = 30 + 0.7x1 + 3x2 Also provided are SST = 1,200 and SSE = 384. -The least squares criterion is

Exhibit 15-7 A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares.SSR = 165 SSE = 60 -Refer to Exhibit 15-7. The test statistic from the information provided is

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -A multiple regression model has the form = 5 + 6x + 7w As x increases by 1 unit (holding w constant), y is expected to

Exhibit 15-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 15-5. The interpretation of the coefficient on x1 is that

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Inference About Means and Proportions With Two Populations

Inferences About Population Variances

Tests of Goodness of Fit, Independence and Multiple Proportions

Experimental Design and Analysis of Variance

Simple Linear Regression

Regression Analysis: Model Building

Time Series Analysis and Forecasting

Nonparametric Methods

Statistical Methods for Quality Control

Decision Analysis

Sample Survey

Filters

In a multiple regression model, the error term $\varepsilon$ is assumed to be a random variable with a mean of

In a multiple regression model, the variance of the error term $\varepsilon$ is assumed to be

Exhibit 15-8 The following estimated regression model was developed relating yearly income (y in $1,000s) of 30 individuals with their age (x₁) and their gender (x₂) (0 if male and 1 if female). = 30 + 0.7x₁ + 3x₂ Also provided are SST = 1,200 and SSE = 384. -The least squares criterion is

Exhibit 15-5 Below you are given a partial Excel output based on a sample of 25 observations. -Refer to Exhibit 15-5. The interpretation of the coefficient on x₁ is that