Question 1

The mathematical equation relating the expected value of the dependent variable to the value of the independent variables, which has the form of E(y) =   is

Accepted Answer

A) a simple linear regression model 
B) a multiple nonlinear regression model 
C) an estimated multiple regression equation 
D) a multiple regression equation 
A) a simple linear regression model 
B) a multiple nonlinear regression model 
C) an estimated multiple regression equation 
D) a multiple regression equation D

Question 2

Multiple regression analysis was used to study how an individual's income (Y in thousands of dollars) is influenced by age (X1 in years), level of education (X2 ranging from 1 to 5), and the person's gender (X3 where 0 =female and 1=male). The following is a partial result of a computer program that was used on a sample of 20 individuals.   
a.Compute the coefficient of determination.
b.Perform a t test and determine whether or not the coefficient of the variable "level of education" (i.e., X2) is significantly different from zero. Let $\alpha$ = 0.05.
c.At $\alpha$ = 0.05, perform an F test and determine whether or not the regression model is significant.
d.As you note the coefficient of X3 is -0.510. Fully interpret the meaning of this coefficient.

Accepted Answer

a.0.4286
b.t = 4.84; p-value < .01; reject H₀; significant (critical t = 2.12)
c.F = 4; p-value is between .025 and .05; reject H₀; significant (critical F = 3.24)
d.Male's income is lower than female's by $510

Question 3

The following results were obtained from a multiple regression analysis.   
a.How many independent variables were involved in this model?
b.How many observations were involved?
c.Determine the F statistic.

Accepted Answer

a.8
b.25
c.2.4

Question 4

The Brock Juice Company has developed a regression model relating sales (Y in $10,000s) with four independent variables. The four independent variables are price per unit (X1, in dollars), competitor's price (X2, in dollars), advertising (X3, in $1,000s) and type of container used (X4) (1 = Cans and 0 = Bottles). Part of the regression results are shown below:   
a.Compute the coefficient of determination and fully interpret its meaning.
b.Is the regression model significant? Explain what your answer implies. Let $\alpha$ = 0.05.
c.What has been the sample size for this analysis?

Accepted Answer

a.0.3135; 31.35% of variation

Question 5

Exhibit 15-5
Below you are given a partial Minitab output based on a sample of 25 observations.  
-Refer to Exhibit 15-5. Carry out the test of significance for the parameter $\beta$1at 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 6

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 regression results 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 95% confidence, test to see if price is a significant variable.e. At 95% confidence, test to see if the number of advertising spots is a significant variable.f. Determine the multiple coefficient of determination.

Accepted Answer

a. @#IMG-DLM& b.16 (rounded from 15.49)
c.F = 80.1

Question 7

The correct relationship between SST, SSR, and SSE is given by

Accepted Answer

A) SSR = SST + SSE 
B) SSR = SST - SSE 
C) SSE = SSR - SST 
D) None of these alternatives is correct. 
A) SSR = SST + SSE 
B) SSR = SST - SSE 
C) SSE = SSR - SST 
D) None of these alternatives is correct.

Question 8

For a multiple regression model, SST = 200 and SSE = 50. The multiple coefficient of determination is

Accepted Answer

A) 0.25 
B) 4.00 
C) 250 
D) 0.75 
A) 0.25 
B) 4.00 
C) 250 
D) 0.75

Question 9

A regression was performed on a sample of 16 observations. The estimated equation is   . The standard errors for the coefficients are Sb1 = 4.2, Sb2 = 5.6, and Sb3 = 2.8. For this model, SST = 3809.6 and SSR = 3285.4. 
a.Compute the appropriate t ratios.
b.Test for the significance of $\beta$1, $\beta$2and $\beta$3at the 5% level of significance.
c.Do you think that any of the variables should be dropped from the model? Explain.
d.Compute R2 and Ra2. Interpret R2.
e.Test the significance of the relationship among the variables at the 5% level of significance.

Accepted Answer

a.t₁ = -3.4, t₃ = 1.2, t₃ = 5.6 b.t_.025 = 2.179

Question 10

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:   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

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).   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 12

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).   Also provided are SST = 1,200 and SSE = 384.
-Refer to Exhibit 15-8. The model

Accepted Answer

A) is significant 
B) is not significant 
C) would be significant is the sample size was larger than 30 
D) None of these alternatives is correct. 
A) is significant 
B) is not significant 
C) would be significant is the sample size was larger than 30 
D) None of these alternatives is correct.

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:   For this model SSR = 3500, SSE = 1500, and the sample size is 18.
-Refer to Exhibit 15-2. To test for the significance of the model, the test statistic F is

Accepted Answer

A) 2.33 
B) 0.70 
C) 17.5 
D) 1.75 
A) 2.33 
B) 0.70 
C) 17.5 
D) 1.75

Question 14

Exhibit 15-6
Below you are given a partial computer 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 15

In order to test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

Accepted Answer

A) 47 and 3 
B) 3 and 47 
C) 2 and 43 
D) 3 and 43 
A) 47 and 3 
B) 3 and 47 
C) 2 and 43 
D) 3 and 43

Question 16

The prices of Rawlston, Inc. stock (y) over a period of 12 days, the number of shares (in 100s) of company's stocks sold (x1), and the volume of exchange (in millions) on the New York Stock Exchange (x2) are shown below.   Excel was used to determine the least-squares regression equation. Part of the computer output is shown below.  
a. Use the output shown above and write an equation that can be used to predict the price of the stock.
b. Interpret the coefficients of the estimated regression equation that you found in Part a.
c. At 95% confidence, determine which variables are significant and which are not.
d. If in a given day, the number of shares of the company that were sold was 94,500 and the volume of exchange on the New York Stock Exchange was 16 million, what would you expect the price of the stock to be?

Accepted Answer

a. @#IMG-DLM& = 118.5055 - 0.0163x₁ - 1.5726x₂ b.As

Question 17

Exhibit 15-3
In a regression model involving 30 observations, the following estimated regression equation was obtained:   For this model SSR = 700 and SSE = 100.
-Refer to Exhibit 15-3. The critical F value at 95% confidence is

Accepted Answer

A) 2.53 
B) 2.69 
C) 2.76 
D) 2.99 
A) 2.53 
B) 2.69 
C) 2.76 
D) 2.99

Question 18

A multiple regression model has the form   As x1 increases by 1 unit (holding x2 constant), y is expected to

Accepted Answer

A) increase by 9 units 
B) decrease by 9 units 
C) increase by 2 units 
D) decrease by 2 units 
A) increase by 9 units 
B) decrease by 9 units 
C) increase by 2 units 
D) decrease by 2 units

Question 19

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 20

The multiple coefficient of determination is

Accepted Answer

A) MSR/MST 
B) MSR/MSE 
C) SSR/SST 
D) SSE/SSR 
A) MSR/MST 
B) MSR/MSE 
C) SSR/SST 
D) SSE/SSR

The mathematical equation relating the expected value of the dependent variable to the value of the independent variables, which has the form of E(y) = is

The following results were obtained from a multiple regression analysis. a.How many independent variables were involved in this model? b.How many observations were involved? c.Determine the F statistic.

The correct relationship between SST, SSR, and SSE is given by

For a multiple regression model, SST = 200 and SSE = 50. The multiple coefficient of determination is

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). Also provided are SST = 1,200 and SSE = 384. -Refer to Exhibit 15-8. The model

Exhibit 15-6 Below you are given a partial computer 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

In order to test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

Exhibit 15-3 In a regression model involving 30 observations, the following estimated regression equation was obtained: For this model SSR = 700 and SSE = 100. -Refer to Exhibit 15-3. The critical F value at 95% confidence is

A multiple regression model has the form As x₁ increases by 1 unit (holding x₂ constant), y is expected to

A variable that cannot be measured in numerical terms is called

The multiple coefficient of determination is

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

Comparing Multiple Proportions, Test of Independence and Goodness of Fit

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

Index Numbers

Decision Analysis on Website

Sample Survey on Website

Filters

Exam 15: Multiple Regression

The mathematical equation relating the expected value of the dependent variable to the value of the independent variables, which has the form of E(y) = is

The following results were obtained from a multiple regression analysis. a.How many independent variables were involved in this model? b.How many observations were involved? c.Determine the F statistic.

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

The correct relationship between SST, SSR, and SSE is given by

For a multiple regression model, SST = 200 and SSE = 50. The multiple coefficient of determination is

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). Also provided are SST = 1,200 and SSE = 384. -Refer to Exhibit 15-8. The model

Exhibit 15-6 Below you are given a partial computer 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

In order to test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

Exhibit 15-3 In a regression model involving 30 observations, the following estimated regression equation was obtained: For this model SSR = 700 and SSE = 100. -Refer to Exhibit 15-3. The critical F value at 95% confidence is

A multiple regression model has the form As x1 increases by 1 unit (holding x2 constant), y is expected to

A variable that cannot be measured in numerical terms is called

The multiple coefficient of determination is

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

Comparing Multiple Proportions, Test of Independence and Goodness of Fit

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

Index Numbers

Decision Analysis on Website

Sample Survey on Website

Filters

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). Also provided are SST = 1,200 and SSE = 384. -Refer to Exhibit 15-8. The model

A multiple regression model has the form As x₁ increases by 1 unit (holding x₂ constant), y is expected to