Question 1

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

Accepted Answer

A) have a mean of 1 
B) have a variance of zero 
C) have a standard deviation of 1 
D) be normally distributed 
A) have a mean of 1 
B) have a variance of zero 
C) have a standard deviation of 1 
D) be normally distributed

Question 2

A student used multiple regression analysis to study how family spending (y) is influenced by income (x1), family size (x2), and additions to savings (x3). The variables y, x1, and x3 are measured in thousands of dollars. The following results were obtained.   Coefficient of determination = 0.946 
a.Write out the estimated regression equation for the relationship between the variables.
b.What can you say about the strength of this relationship?
c.Carry out a test of whether y is significantly related to the independent variables. Use a .05 level of significance.
d.Carry out a test to see if x3 and y are significantly related. Use a .05 level of significance.
e.Why would a coefficient of determination very close to 1.0 be expected here?

Accepted Answer

a.= 0.0136 + 0.7992x₁ + 0.228x₂ - 0.5796x₃

Question 3

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.
-Refer to Exhibit 15-8. From the above function, it can be said that the expected yearly income of

Accepted Answer

A) males is $3 more than females 
B) females is $3 more than males 
C) males is $3,000 more than females 
D) females is $3,000 more than males 
A) males is $3 more than females 
B) females is $3 more than males 
C) males is $3,000 more than females 
D) females is $3,000 more than males

Question 4

The numerical value of the coefficient of determination

Accepted Answer

A) is always larger than the coefficient of correlation 
B) is always smaller than the coefficient of correlation 
C) is negative if the coefficient of determination is negative 
D) can be larger or smaller than the coefficient of correlation 
A) is always larger than the coefficient of correlation 
B) is always smaller than the coefficient of correlation 
C) is negative if the coefficient of determination is negative 
D) can be larger or smaller than the coefficient of correlation

Question 5

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 order to test for the significance of a regression model involving 4 independent variables and 36 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

Accepted Answer

A) 4 and 36 
B) 3 and 35 
C) 4 and 31 
D) 4 and 32 
A) 4 and 36 
B) 3 and 35 
C) 4 and 31 
D) 4 and 32

Question 6

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.
-Refer to Exhibit 15-8. The test statistic for testing the significance of the model is

Accepted Answer

A) 0.73 
B) 1.47 
C) 28.69 
D) 5.22 
A) 0.73 
B) 1.47 
C) 28.69 
D) 5.22

Question 7

Exhibit 15-3
In a regression model involving 30 observations, the following estimated regression equation was obtained:   = 17 + 4xS1U1B11S1U1B0 - 3xS1U1B12S1U1B0 + 8xS1U1B13S1U1B0 + 8xS1U1B14S1U1B0
For this model SSR = 700 and SSE = 100.
-Refer to Exhibit 15-3. The coefficient of determination for the above model is approximately

Accepted Answer

A) -0.875 
B) 0.875 
C) 0.125 
D) 0.144 
A) -0.875 
B) 0.875 
C) 0.125 
D) 0.144

Question 8

The ratio of MSE/MSR yields

Accepted Answer

A) SST 
B) the F statistic 
C) SSR 
D) None of these alternatives is correct. 
A) SST 
B) the F statistic 
C) SSR 
D) None of these alternatives is correct.

Question 9

Exhibit 15-6
Below you are given a partial Excel output based on a sample of 16 observations.  
-A term used to describe the case when the independent variables in a multiple regression model are correlated is

Accepted Answer

A) regression 
B) correlation 
C) multicollinearity 
D) None of the alternative answers are correct. 
A) regression 
B) correlation 
C) multicollinearity 
D) None of the alternative answers are correct.

Question 10

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 coefficient of determination is

Accepted Answer

A) 0.3636 
B) 0.7333 
C) 0.275 
D) 0.5 
A) 0.3636 
B) 0.7333 
C) 0.275 
D) 0.5

Question 11

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. If we want to test for the significance of the regression model, the critical value of F at 95% confidence is

Accepted Answer

A) 3.68 
B) 3.29 
C) 3.24 
D) 4.54 
A) 3.68 
B) 3.29 
C) 3.24 
D) 4.54

Question 12

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 of significance for the parameter $\beta$1 at the 1% 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 13

Exhibit 15-6
Below you are given a partial Excel output based on a sample of 16 observations.  
-Refer to Exhibit 15-6. The degrees of freedom for the sum of squares explained by the regression (SSR) are

Accepted Answer

A) 2 
B) 3 
C) 13 
D) 15 
A) 2 
B) 3 
C) 13 
D) 15

Question 14

The following regression model has been proposed to predict sales at a computer store.   = 50 - 3x1 + 20x2 + 10x3
where
x1 = competitor's previous day's sales (in $1,000s)
x2 = population within 1 mile (in 1,000s)     = sales (in $1000s)
Predict sales (in dollars) for a store with the competitor's previous day's sale of $5,000, a population of 20,000 within 1 mile, and nine radio advertisements.

Accepted Answer

Question 15

In regression analysis, an outlier is an observation whose

Accepted Answer

A) mean is larger than the standard deviation 
B) residual is zero 
C) mean is zero 
D) residual is much larger than the rest of the residual values 
A) mean is larger than the standard deviation 
B) residual is zero 
C) mean is zero 
D) residual is much larger than the rest of the residual values

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.
-In order to test for the significance of a regression model involving 8 independent variables and 121 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

Accepted Answer

A) 8 and 121 
B) 7 and 120 
C) 8 and 112 
D) 7 and 112 
A) 8 and 121 
B) 7 and 120 
C) 8 and 112 
D) 7 and 112

Question 17

A regression analysis involved 17 independent variables and 697 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

Accepted Answer

A) 696 degrees of freedom 
B) 16 degrees of freedom 
C) 713 degrees of freedom 
D) 714 degrees of freedom 
A) 696 degrees of freedom 
B) 16 degrees of freedom 
C) 713 degrees of freedom 
D) 714 degrees of freedom

Question 18

Exhibit 15-6
Below you are given a partial Excel output based on a sample of 16 observations.  
-Refer to Exhibit 15-6. The t value obtained from the table which is used to test an individual parameter at the 1% level is

Accepted Answer

A) 2.65 
B) 2.921 
C) 2.977 
D) 3.012 
A) 2.65 
B) 2.921 
C) 2.977 
D) 3.012

Question 19

Exhibit 15-3
In a regression model involving 30 observations, the following estimated regression equation was obtained:   = 17 + 4xS1U1B11S1U1B0 - 3xS1U1B12S1U1B0 + 8xS1U1B13S1U1B0 + 8xS1U1B14S1U1B0
For this model SSR = 700 and SSE = 100.
-Refer to Exhibit 15-3. The conclusion is that the

Accepted Answer

A) model is not significant 
B) model is significant 
C) slope of x1 is significant 
D) slope of x2 is significant 
A) model is not significant 
B) model is significant 
C) slope of x1 is significant 
D) slope of x2 is significant

Question 20

Exhibit 15-6
Below you are given a partial Excel output based on a sample of 16 observations.  
-Refer to Exhibit 15-6. The sum of squares due to error (SSE) equals

Accepted Answer

A) 37.33 
B) 485.3 
C) 4,853 
D) 6,308.9 
A) 37.33 
B) 485.3 
C) 4,853 
D) 6,308.9

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

The numerical value of the coefficient of determination

Exhibit 15-3 In a regression model involving 30 observations, the following estimated regression equation was obtained: = 17 + 4x₁ - 3x₂ + 8x₃ + 8x₄ For this model SSR = 700 and SSE = 100. -Refer to Exhibit 15-3. The coefficient of determination for the above model is approximately

The ratio of MSE/MSR yields

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -A term used to describe the case when the independent variables in a multiple regression model are correlated 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 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. The degrees of freedom for the sum of squares explained by the regression (SSR) are

In regression analysis, an outlier is an observation whose

A regression analysis involved 17 independent variables and 697 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. The t value obtained from the table which is used to test an individual parameter at the 1% level is

Exhibit 15-3 In a regression model involving 30 observations, the following estimated regression equation was obtained: = 17 + 4x₁ - 3x₂ + 8x₃ + 8x₄ For this model SSR = 700 and SSE = 100. -Refer to Exhibit 15-3. The conclusion is that the

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. The sum of squares due to error (SSE) equals

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

The numerical value of the coefficient of determination

Exhibit 15-3 In a regression model involving 30 observations, the following estimated regression equation was obtained: = 17 + 4x1 - 3x2 + 8x3 + 8x4 For this model SSR = 700 and SSE = 100. -Refer to Exhibit 15-3. The coefficient of determination for the above model is approximately

The ratio of MSE/MSR yields

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -A term used to describe the case when the independent variables in a multiple regression model are correlated 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 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 of significance for the parameter β\betaβ 1 at the 1% level. The null hypothesis should be

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. The degrees of freedom for the sum of squares explained by the regression (SSR) are

In regression analysis, an outlier is an observation whose

A regression analysis involved 17 independent variables and 697 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. The t value obtained from the table which is used to test an individual parameter at the 1% level is

Exhibit 15-3 In a regression model involving 30 observations, the following estimated regression equation was obtained: = 17 + 4x1 - 3x2 + 8x3 + 8x4 For this model SSR = 700 and SSE = 100. -Refer to Exhibit 15-3. The conclusion is that the

Exhibit 15-6 Below you are given a partial Excel output based on a sample of 16 observations. -Refer to Exhibit 15-6. The sum of squares due to error (SSE) equals

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

Exhibit 15-3 In a regression model involving 30 observations, the following estimated regression equation was obtained: = 17 + 4x₁ - 3x₂ + 8x₃ + 8x₄ For this model SSR = 700 and SSE = 100. -Refer to Exhibit 15-3. The coefficient of determination for the above model is approximately

Exhibit 15-3 In a regression model involving 30 observations, the following estimated regression equation was obtained: = 17 + 4x₁ - 3x₂ + 8x₃ + 8x₄ For this model SSR = 700 and SSE = 100. -Refer to Exhibit 15-3. The conclusion is that the