Question 1

In multiple regression analysis,

Accepted Answer

A) there can be any number of dependent variables but only one independent variable 
B) there must be only one independent variable 
C) the coefficient of determination must be larger than 1 
D) there can be several independent variables, but only one dependent variable 
A) there can be any number of dependent variables but only one independent variable 
B) there must be only one independent variable 
C) the coefficient of determination must be larger than 1 
D) there can be several independent variables, but only one dependent variable

Question 2

Below you are given a partial Excel output based on a sample of 30 days of the price of a company's stock (y in dollars), the Dow Jones industrial average (x1), and the stock price of the company's major competitor (x2 in dollars).   
a.Use the output shown above and write an equation that can be used to predict the price of the stock.
b.If the Dow Jones Industrial Average is 2650 and the price of the competitor is $45, what would you expect the price of the stock to be?
c.At $\alpha$ = 0.05, test to determine if the Dow Jones average is a significant variable.
d.At $\alpha$ = 0.05, test to determine if the stock price of the major competitor is a significant variable.

Accepted Answer

a.= 20 + 0.03x₁ - 0

Question 3

In a regression model involving 46 observations, the following estimated regression equation was obtained.   = 17 + 4x1 - 3x2 + 8x3 + 5x4 + 8x5
For this model, SST = 3410 and SSE = 510. 
a.Compute the coefficient of determination.
b.Perform an F test and determine whether or not the regression model is significant.

Accepted Answer

a.0.85
b.F

Question 4

Exhibit 15-6
Below you are given a partial Excel output based on a sample of 16 observations.  
-Refer to Exhibit 15-6. The F value obtained from the table used to test if there is a relationship among the variables at the 5% level equals

Accepted Answer

A) 3.41 
B) 3.63 
C) 3.81 
D) 19.41 
A) 3.41 
B) 3.63 
C) 3.81 
D) 19.41

Question 5

The following is part of the results of a regression analysis involving sales (y in millions of dollars), advertising expenditures (x1 in thousands of dollars), and number of salespeople (x2) for a corporation. The regression was performed on a sample of 10 observations.   
a.If the company uses $40,000 in advertisement and has 30 salespersons, what are the expected sales? Give your answer in dollars.
b.At $\alpha$ = 0.05, test for the significance of the coefficient of advertising.
c.At $\alpha$ = 0.05, test for the significance of the coefficient of the number of salespeople.

Accepted Answer

a.$540,000,000
b.t = 3.2 > 2.3

Question 6

Exhibit 15-6
Below you are given a partial Excel output based on a sample of 16 observations.  
-Refer to Exhibit 15-6. The test statistic used to determine if there is a relationship among the variables equals

Accepted Answer

A) -1.4 
B) 0.2 
C) 0.77 
D) 5 
A) -1.4 
B) 0.2 
C) 0.77 
D) 5

Question 7

In order to determine whether or not the number of automobiles sold per day (y) is related to price (x1 in $1,000), and the number of advertising spots (x2), data were gathered for 7 days. Part of the Excel output is shown below.   
a.Determine the least squares regression function relating y to x1 and x2.
b.If the company charges $20,000 for each car and uses 10 advertising spots, how many cars would you expect them to sell in a day?
c.At $\alpha$ = 0.05, test to determine if the fitted equation developed in Part a represents a significant relationship between the independent variables and the dependent variable.
d.At $\alpha$ = 0.05, test to see if $\beta$1 is significantly different from zero.
e.Determine the multiple coefficient of determination.

Accepted Answer

a.= 0.8051 + 0.4977x₁

Question 8

Exhibit 15-6
Below you are given a partial Excel output based on a sample of 16 observations.  
-A variable that cannot be measured in numerical terms is called

Accepted Answer

A) a nonmeasurable random variable 
B) a constant variable 
C) a dependent variable 
D) a qualitative variable 
A) a nonmeasurable random variable 
B) a constant variable 
C) a dependent variable 
D) a qualitative variable

Question 9

A regression model involved 5 independent variables and 126 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

Accepted Answer

A) 131 degrees of freedom 
B) 125 degrees of freedom 
C) 130 degrees of freedom 
D) 4 degrees of freedom 
A) 131 degrees of freedom 
B) 125 degrees of freedom 
C) 130 degrees of freedom 
D) 4 degrees of freedom

Question 10

The following is part of the results of a regression analysis involving sales (y in millions of dollars), advertising expenditures (x1 in thousands of dollars), and number of sales people (x2) for a corporation:   
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.
d.What has been the sample size for this regression analysis?

Accepted Answer

a.F = 3.91 < 4.74; n

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 analysis involved 6 independent variables and 27 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

Accepted Answer

A) 27 degrees of freedom 
B) 26 degrees of freedom 
C) 21 degrees of freedom 
D) 20 degrees of freedom 
A) 27 degrees of freedom 
B) 26 degrees of freedom 
C) 21 degrees of freedom 
D) 20 degrees of freedom

Question 12

In a multiple regression analysis involving 15 independent variables and 200 observations, SST = 800 and SSE = 240. The coefficient of determination is

Accepted Answer

A) 0.300 
B) 0.192 
C) 0.500 
D) 0.700 
A) 0.300 
B) 0.192 
C) 0.500 
D) 0.700

Question 13

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 multiple coefficient of determination for this problem is

Accepted Answer

A) 0.4368 
B) 0.6960 
C) 0.3040 
D) 0.2289 
A) 0.4368 
B) 0.6960 
C) 0.3040 
D) 0.2289

Question 14

For a multiple regression model, SSR = 600 and SSE = 200. The multiple coefficient of determination is

Accepted Answer

A) 0.333 
B) 0.275 
C) 0.300 
D) 0.75 
A) 0.333 
B) 0.275 
C) 0.300 
D) 0.75

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.
-In a multiple regression analysis involving 5 independent variables and 30 observations, SSR = 360 and SSE = 40. The coefficient of determination is

Accepted Answer

A) 0.80 
B) 0.90 
C) 0.25 
D) 0.15 
A) 0.80 
B) 0.90 
C) 0.25 
D) 0.15

Question 16

Exhibit 15-6
Below you are given a partial Excel output based on a sample of 16 observations.  
-Refer to Exhibit 15-6. Carry out the test to determine if there is a relationship among the variables at the 5% level. The null hypothesis should

Accepted Answer

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

Question 17

A regression was performed on a sample of 20 observations. Two independent variables were included in the analysis, x and z. The relationship between x and z is z = x2. The following estimated equation was obtained.   = 23.72 + 12.61x + 0.798z
The standard errors for the coefficients are Sb1 = 4.85 and Sb2 = 0.21
For this model, SSR = 520.2 and SSE = 340.6 
a.Estimate the value of y when x = 5.
b.Compute the appropriate t ratios.
c.Test for the significance of the coefficients at the 5% level. Which variable(s) is (are) significant?
d.Compute the coefficient of determination and the adjusted coefficient of determination. Interpret the meaning of the coefficient of determination.
e.Test the significance of the relationship among the variables at the 5% level of significance.

Accepted Answer

a.106.72 b.2.6, 3.8 c.t_.025 = 2.11 Both x an

Question 18

Exhibit 15-4
a.y = $\beta$S1U1B10S1U1B0 + $\beta$S1U1B11S1U1B0xS1U1B11S1U1B0 + $\beta$S1U1B12S1U1B0xS1U1B12S1U1B0 + $\varepsilon$
b.E(y) = $\beta$S1U1B10S1U1B0 + $\beta$S1U1B11S1U1B0xS1U1B11S1U1B0 + $\beta$S1U1B12S1U1B0xS1U1B12S1U1B0
c.= bS1U1B1oS1U1B0 + bS1U1B11S1U1B0 xS1U1B11S1U1B0 + bS1U1B12S1U1B0 xS1U1B12S1U1B0
d.E(y) = $\beta$S1U1B10S1U1B0 + $\beta$S1U1B11S1U1B0xS1U1B11S1U1B0 + $\beta$S1U1B12S1U1B0xS1U1B12S1U1B0
-Refer to Exhibit 15-4. Which equation describes the multiple regression model?

Accepted Answer

A) equation a 
B) equation b 
C) equation c 
D) equation d 
A) equation a 
B) equation b 
C) equation c 
D) equation d

Question 19

Exhibit 15-6
Below you are given a partial Excel output based on a sample of 16 observations.  
-Refer to Exhibit 15-6. The estimated regression equation is

Accepted Answer

A) y = $\beta$0 + $\beta$1x1 + $\beta$2x2 + $\varepsilon$ 
B) E(y) = $\beta$0 + $\beta$1x1 + $\beta$2x2 
C) = 12.924 - 3.682 x1 + 45.216 x2 
D) = 4.425 + 2.63 x1 + 12.56 x2 
A) y = $\beta$0 + $\beta$1x1 + $\beta$2x2 + $\varepsilon$ 
B) E(y) = $\beta$0 + $\beta$1x1 + $\beta$2x2 
C) = 12.924 - 3.682 x1 + 45.216 x2 
D) = 4.425 + 2.63 x1 + 12.56 x2

Question 20

A variable that takes on the values of 0 or 1 and is used to incorporate the effect of qualitative variables in a regression model is called

Accepted Answer

A) an interaction 
B) a constant variable 
C) a dummy variable 
D) None of these alternatives is correct. 
A) an interaction 
B) a constant variable 
C) a dummy variable 
D) None of these alternatives is correct.

In multiple regression analysis,

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. The F value obtained from the table used to test if there is a relationship among the variables at the 5% level equals

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. The test statistic used to determine if there is a relationship among the variables equals

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -A variable that cannot be measured in numerical terms is called

A regression model involved 5 independent variables and 126 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

In a multiple regression analysis involving 15 independent variables and 200 observations, SST = 800 and SSE = 240. The coefficient of determination is

For a multiple regression model, SSR = 600 and SSE = 200. The multiple coefficient of determination is

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. Carry out the test to determine if there is a relationship among the variables at the 5% level. The null hypothesis should

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. The estimated regression equation is

A variable that takes on the values of 0 or 1 and is used to incorporate the effect of qualitative variables in a regression model is called

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

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Exam 15: Multiple Regression

In multiple regression analysis,

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. The F value obtained from the table used to test if there is a relationship among the variables at the 5% level equals

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. The test statistic used to determine if there is a relationship among the variables equals

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -A variable that cannot be measured in numerical terms is called

A regression model involved 5 independent variables and 126 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

In a multiple regression analysis involving 15 independent variables and 200 observations, SST = 800 and SSE = 240. The coefficient of determination is

For a multiple regression model, SSR = 600 and SSE = 200. The multiple coefficient of determination is

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. Carry out the test to determine if there is a relationship among the variables at the 5% level. The null hypothesis should

Exhibit 15-4 a.y = β\betaβ 0 + β\betaβ 1x1 + β\betaβ 2x2 + ε\varepsilonε b.E(y) = β\betaβ 0 + β\betaβ 1x1 + β\betaβ 2x2 c.= bo + b1 x1 + b2 x2 d.E(y) = β\betaβ 0 + β\betaβ 1x1 + β\betaβ 2x2 -Refer to Exhibit 15-4. Which equation describes the multiple regression model?

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. The estimated regression equation is

A variable that takes on the values of 0 or 1 and is used to incorporate the effect of qualitative variables in a regression model is called

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