Question 1

Determine the value of   .

Accepted Answer

A) 0.2523 
B) 1.43 
C) 0.202 
D) 0.17609 
A) 0.2523 
B) 1.43 
C) 0.202 
D) 0.17609

Question 2

In multiple regression analysis,dummy variables are added to the regression model to control the error of the estimate.

Accepted Answer

A) True 
 B)False

Question 3

The two regressions Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + ε and Y = β0 + β1X1 + β2X2 + ε were run using a sample of 60 observations.If the SSE for the first regression is 1,688.4,what would you expect the SSE for the second regression be?

Accepted Answer

A) SSE = 1,688.4 
B) SSE < 1,688.4 
C) SSE ≥ 1,688.4 
D) SSE < 688.4 
A) SSE = 1,688.4 
B) SSE < 1,688.4 
C) SSE ≥ 1,688.4 
D) SSE < 688.4

Question 4

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Suppose you are interested in determining the factors that influence the time required to prepare a tax return.You develop the model Y = βS1U1B10S1U1B0 + βS1U1B11S1U1B0XS1U1B11S1U1B0 + βS1U1B12S1U1B0XS1U1B12S1U1B0 + βS1U1B13S1U1B0
S1U1B1 S1U1B0
   
+ βS1U1B14S1U1B0XS1U1B13S1U1B0 + βS1U1B15S1U1B0XS1U1B14S1U1B0S1U1B1 S1U1B0+ βS1U1B16S1U1B0(XS1U1B11S1U1B0 ∙ XS1U1B14S1U1B0)S1U1B1 S1U1B0+ ε,where Y is the amount of time in minutes,XS1U1B11S1U1B0 is the income of the individual (in thousands of dollars),XS1U1B12S1U1B0 is the age of the individual,XS1U1B13S1U1B0 is the number of people living in the household,and XS1U1B14S1U1B0 is a dummy variable that takes the value 1 if the individual owns his or her own home.After interviewing 40 accountants,you obtained   
= 17.2 + 0.38xS1U1B11S1U1B0 + 1.04xS1U1B12S1U1B0 - 0.04   
+ 2.15xS1U1B13S1U1B0 + 0.11xS1U1B14S1U1B0 - 0.22(xS1U1B11S1U1B0 ∙ xS1U1B14S1U1B0),   
= 5.3,   
= 0.13,   
= 0.33,   
= 1.51,   
= 4.7,   
= 0.05,and   
= 0.07.
-Test the hypothesis H0 : β2 = 0 and interpret your result.

Accepted Answer

t = @#IMG-DLM& 
(j = 1,2,... ,K)
t = @#IMG-DLM& 
= 3.15
Sinc

Question 5

The adjusted coefficient of determination,   
2,compared to R2,provides a better comparison between multiple regression models with different numbers of independent variables.

Accepted Answer

A) True 
 B)False

Question 6

The multiple coefficient of determination R2 can only be used to compare regression models that have the same set of sample observations of yi,where i =1,2,…,n.

Accepted Answer

A) True 
 B)False

Question 7

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Suppose you are interested in determining the factors that influence the time required to prepare a tax return,and developed the model: Y = βS1U1B10S1U1B0 + βS1U1B11S1U1B0XS1U1B11S1U1B0 + βS1U1B12S1U1B0XS1U1B12S1U1B0 + βS1U1B13S1U1B0XS1U1B13S1U1B0 + βS1U1B14S1U1B0XS1U1B14S1U1B0 + ε,where Y is the amount of time (in minutes),XS1U1B11S1U1B0 is the income of the individual (in thousands of dollars),XS1U1B12S1U1B0 is the age of the individual,XS1U1B13S1U1B0 is the number of people living in the household,and XS1U1B14S1U1B0 is a dummy variable that takes the value 1,if the individual owns his or her own home.After interviewing 40 accountants,you get the following results:   
= 17.2 + 3.8xS1U1B11S1U1B0 - 1.04xS1U1B12S1U1B0 + 2.15xS1U1B13S1U1B0 + 15.1xS1U1B14S1U1B0,   
= 5.3,   
= 0.13,   
= 0.33,   
= 1.51,   
= 4.7,SSR = 164.2,SSE = 200.7,and RS1U1P12S1S1P0 = 0.45.
-Test for H0 : β1 = β2 = β3 = β4 = 0 and interpret your result.

Accepted Answer

SSR = 164.2 and SSE = 200.7
F = @#IMG-DLM& 
= @#IMG-DLM& 
=

Question 8

The F- and t-tests will always provide the same conclusions regarding the hypothesis test for a single independent variable in a multiple regression model.

Accepted Answer

A) True 
 B)False

Question 9

In a multiple regression analysis involving K independent variables and n data points,the number of degrees of freedom associated with the sum of squares for error is:

Accepted Answer

A) K-1 
B) n - K 
C) n - 1 
D) n - K - 1 
A) K-1 
B) n - K 
C) n - 1 
D) n - K - 1

Question 10

If a dummy variable for gender is to be included in a multiple regression model,"female" would be coded as 1 and "male" would be coded as 2.

Accepted Answer

A) True 
 B)False

Question 11

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Suppose you are interested in determining the factors that influence the time required to prepare a tax return,and developed the model: Y = βS1U1B10S1U1B0 + βS1U1B11S1U1B0XS1U1B11S1U1B0 + βS1U1B12S1U1B0XS1U1B12S1U1B0 + βS1U1B13S1U1B0XS1U1B13S1U1B0 + βS1U1B14S1U1B0XS1U1B14S1U1B0 + ε,where Y is the amount of time (in minutes),XS1U1B11S1U1B0 is the income of the individual (in thousands of dollars),XS1U1B12S1U1B0 is the age of the individual,XS1U1B13S1U1B0 is the number of people living in the household,and XS1U1B14S1U1B0 is a dummy variable that takes the value 1,if the individual owns his or her own home.After interviewing 40 accountants,you get the following results:   
= 17.2 + 3.8xS1U1B11S1U1B0 - 1.04xS1U1B12S1U1B0 + 2.15xS1U1B13S1U1B0 + 15.1xS1U1B14S1U1B0,   
= 5.3,   
= 0.13,   
= 0.33,   
= 1.51,   
= 4.7,SSR = 164.2,SSE = 200.7,and RS1U1P12S1S1P0 = 0.45.
-Interpret the estimated regression coefficient b4.

Accepted Answer

If the person owns his or her own home,w

Question 12

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A regression analysis has produced the following partial analysis of variance table:
Analysis of Variance
  
-Compute the proportion of the total sample variability that is explained by the regression.

Accepted Answer

R² = SSR /

Question 13

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A researcher is interested in determining the monthly household expenditures on groceries.He models the relationship as follows: Y = βS1U1B10S1U1B0 + βS1U1B11S1U1B0XS1U1B11S1U1B0 + βS1U1B12S1U1B0XS1U1B12S1U1B0 + βS1U1B13S1U1B0XS1U1B13S1U1B0 + ε,where Y is the monthly dollar value spent on groceries,XS1U1B11S1U1B0 is the household's monthly income,XS1U1B12S1U1B0 is the number of people living in the household,and XS1U1B13S1U1B0S1U1B1 S1U1B0is a dummy variable = 1 if both the adults in the household work.Taking a sample of 250 households,the researcher gets the following results:   
= 172.1 + 0.048xS1U1B11S1U1B0 + 33.1xS1U1B12S1U1B0 + 43.2xS1U1B13S1U1B0.
-How should the researcher interpret the coefficient of the dummy variable?

Accepted Answer

A) Households with both adults working approximately spend $43.20 on groceries,under the assumption that all the other independent variables in the model are held constant. 
B) Households with both adults working spend,on average,$43.20 less than other households,under the assumption that all the other independent variables in the model are held constant. 
C) Households with both adults working spend,on average,$43.20 more than other households,under the assumption that all the other independent variables in the model are held constant. 
D) There is no difference between the types of households and their spending on groceries,under the assumption that all the other independent variables in the model are held constant. 
A) Households with both adults working approximately spend $43.20 on groceries,under the assumption that all the other independent variables in the model are held constant. 
B) Households with both adults working spend,on average,$43.20 less than other households,under the assumption that all the other independent variables in the model are held constant. 
C) Households with both adults working spend,on average,$43.20 more than other households,under the assumption that all the other independent variables in the model are held constant. 
D) There is no difference between the types of households and their spending on groceries,under the assumption that all the other independent variables in the model are held constant.

Question 14

In multiple regression,to test H0 : β1 = β2 = ∙ ∙ ∙ ∙ ∙ ∙ = βk = 0,a t-statistic with n - K degrees of freedom is used.

Accepted Answer

A) True 
 B)False

Question 15

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The model y = βS1U1B10S1U1B0 + βS1U1B11S1U1B0XS1U1B11S1U1B0 + βS1U1B12S1U1B0XS1U1B12S1U1B0 + ε was fitted to a sample of 25 families in order to explain household milk consumption: where y = Milk consumption,in quarts,per week,xS1U1B11S1U1B0 = Weekly income,in hundreds of dollars,and xS1U1B12S1U1B0S1U1B1 S1U1B0= Family size.The least squares estimates of the regression parameters were bS1U1B10S1U1B0 = -0.03,bS1U1B11S1U1B0 = 0.05,and bS1U1B12S1U1B0 = 1.1,with coefficient standard errors   
= 0.02;   
= 0.38.The total sum of squares and the error sum of squares were found to be 165.8 and 66.32 respectively.
-Find the adjusted coefficient of determination.

Accepted Answer

@#IMG-DLM& ² = 1 - @#IMG-DLM&

Question 16

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Assume that xS1U1B11S1U1B0 is a continuous variable and xS1U1B12S1U1B0 is a dummy variable with a value of 0 or 1.
-Consider the following statistics of a multiple regression model: n = 25,K = 5,b1 = -6.31,and   
= 2.98.Can we conclude at the 1% significance level that x1 and y are linearly related?

Accepted Answer

H₀ : β₁ = 0_, against H₁ : β₁≠ 0 t =

Question 17

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
An actuary wanted to develop a model to predict how long individuals will live.After consulting a number of physicians,she collected the age at death (y),the average number of hours of exercise per week (xS1U1B11S1U1B0),the cholesterol level (xS1U1B12S1U1B0),and the number of points that the individual's blood pressure exceeded the recommended value (xS1U1B13S1U1B0).A random sample of 40 individuals was selected.The computer output of the multiple regression model is shown below.
THE REGRESSION EQUATION IS:   
= 55.8 + 1.79xS1U1B11S1U1B0 - 0.021xS1U1B12S1U1B0 - 0.016xS1U1B13S1U1B0
   
S = 9.47 R-Sq = 22.5%
ANALYSIS OF VARIANCE
  
-Is there enough evidence at the 1% significance level to infer that the average number of hours of exercise per week and the age at death are linearly related?

Accepted Answer

H₀ : β₁= 0 against H₁ : β₁≠ 0 Rejection regi

Question 18

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A loan officer is interested in examining the determinants of the total dollar value of residential loans made during a month.She used Y = βS1U1B10S1U1B0 + βS1U1B11S1U1B0XS1U1B11S1U1B0 + βS1U1B12S1U1B0XS1U1B12S1U1B0 + βS1U1B13S1U1B0XS1U1B13S1U1B0 + βS1U1B14S1U1B0XS1U1B14S1U1B0 + ε to model the relationship,where Y is the total dollar value of residential loans in a month (in millions of dollars),XS1U1B11S1U1B0S1U1B1 S1U1B0is the number of loans,XS1U1B12S1U1B0S1U1B1 S1U1B0is the interest rate,XS1U1B13S1U1B0 is the dollar value of expenditures of the bank on advertising (in thousands of dollars),and XS1U1B14S1U1B0 is a dummy variable equal to 1 if the observation is either June,July,or August.
-Suppose that she obtained   = 3.8 + 0.23x1 - 1.31x2 + 0.032x3 + 1.05x4 by using data from the past 24 months.How would we interpret the coefficient on x4?

Accepted Answer

A) On an average,we would expect an additional 1.05 loans per month during June,July,and August. 
B) On an average,we would expect an additional $1.05 million in loans during June,July,and August. 
C) On an average,we would expect an additional 1.05% increase in loans during June,July,and August. 
D) There is no difference in the total residential loan amount between the months of June and September. 
A) On an average,we would expect an additional 1.05 loans per month during June,July,and August. 
B) On an average,we would expect an additional $1.05 million in loans during June,July,and August. 
C) On an average,we would expect an additional 1.05% increase in loans during June,July,and August. 
D) There is no difference in the total residential loan amount between the months of June and September.

Question 19

The manager's null and alternative hypotheses for β1 is:

Accepted Answer

A) H0 : β1 = 0 and H1 : β1 > 0. B) H0 : β1 > 0 and H1 : β1 0 : β1 ≠ 0 and H1 : β1 = 0. D) H0 : β1 = 0 and H1 : 0 1 < 1. A) H0 : β1 = 0 and H1 : β1 > 0. B) H0 : β1 > 0 and H1 : β1 0 : β1 ≠ 0 and H1 : β1 = 0. D) H0 : β1 = 0 and H1 : 0 1 < 1.

Question 20

Determine the regression equation.

Accepted Answer

A)    
profit = 0.2432 + 0.0201 year + 0.2523 X1 revenue - 0.0001 X2 offices 
B)    
profit = 0.2432 + 0.2523 year + 0.0201 X1 revenue - 0.0001 X2 offices 
C)    
profit = 0.000070 + 0.2523 year + 0.0201 X1 revenue - 0.24 X2 offices 
D)    
profit = 0.000070 + 0.0201 year + 0.252 X1 revenue - 0.24 X2 offices 
A)    
profit = 0.2432 + 0.0201 year + 0.2523 X1 revenue - 0.0001 X2 offices 
B)    
profit = 0.2432 + 0.2523 year + 0.0201 X1 revenue - 0.0001 X2 offices 
C)    
profit = 0.000070 + 0.2523 year + 0.0201 X1 revenue - 0.24 X2 offices 
D)    
profit = 0.000070 + 0.0201 year + 0.252 X1 revenue - 0.24 X2 offices

Determine the value of .

In multiple regression analysis,dummy variables are added to the regression model to control the error of the estimate.

The two regressions Y = β₀ + β₁X₁ + β₂X₂ + β₃X₃ + β₄X₄ + ε and Y = β₀ + β₁X₁ + β₂X₂ + ε were run using a sample of 60 observations.If the SSE for the first regression is 1,688.4,what would you expect the SSE for the second regression be?

The adjusted coefficient of determination, ²,compared to R²,provides a better comparison between multiple regression models with different numbers of independent variables.

The multiple coefficient of determination R² can only be used to compare regression models that have the same set of sample observations of y_i,where i =1,2,…,n.

The F- and t-tests will always provide the same conclusions regarding the hypothesis test for a single independent variable in a multiple regression model.

In a multiple regression analysis involving K independent variables and n data points,the number of degrees of freedom associated with the sum of squares for error is:

If a dummy variable for gender is to be included in a multiple regression model,"female" would be coded as 1 and "male" would be coded as 2.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A regression analysis has produced the following partial analysis of variance table: Analysis of Variance -Compute the proportion of the total sample variability that is explained by the regression.

In multiple regression,to test H₀ : β₁= β₂ = ∙ ∙ ∙ ∙ ∙ ∙ = β_k= 0,a t-statistic with n - K degrees of freedom is used.

The manager's null and alternative hypotheses for β₁is:

Determine the regression equation.

Describing Data: Graphical

Describing Data: Numerical

Probability

Discrete Random Variables and Probability Distributions

Continuous Random Variables and Probability Distributions

Sampling and Sampling Distributions

Estimation: Single Population

Estimation: Additional Topics

Hypothesis Testing: Single Population

Hypothesis Testing: Additional Topics

Simple Regression

Additional Topics in Regression Analysis

Analysis of Categorical Data

Analysis of Variance

Time-Series Analysis and Forecasting

Additional Topics in Sampling

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Exam 12: Multiple Regression

Determine the value of .

In multiple regression analysis,dummy variables are added to the regression model to control the error of the estimate.

The two regressions Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + ε and Y = β0 + β1X1 + β2X2 + ε were run using a sample of 60 observations.If the SSE for the first regression is 1,688.4,what would you expect the SSE for the second regression be?

The adjusted coefficient of determination, 2,compared to R2,provides a better comparison between multiple regression models with different numbers of independent variables.

The multiple coefficient of determination R2 can only be used to compare regression models that have the same set of sample observations of yi,where i =1,2,…,n.

The F- and t-tests will always provide the same conclusions regarding the hypothesis test for a single independent variable in a multiple regression model.

In a multiple regression analysis involving K independent variables and n data points,the number of degrees of freedom associated with the sum of squares for error is:

If a dummy variable for gender is to be included in a multiple regression model,"female" would be coded as 1 and "male" would be coded as 2.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A regression analysis has produced the following partial analysis of variance table: Analysis of Variance -Compute the proportion of the total sample variability that is explained by the regression.

In multiple regression,to test H0 : β1 = β2 = ∙ ∙ ∙ ∙ ∙ ∙ = βk = 0,a t-statistic with n - K degrees of freedom is used.

The manager's null and alternative hypotheses for β1 is:

Determine the regression equation.

Describing Data: Graphical

Describing Data: Numerical

Probability

Discrete Random Variables and Probability Distributions

Continuous Random Variables and Probability Distributions

Sampling and Sampling Distributions

Estimation: Single Population

Estimation: Additional Topics

Hypothesis Testing: Single Population

Hypothesis Testing: Additional Topics

Simple Regression

Additional Topics in Regression Analysis

Analysis of Categorical Data

Analysis of Variance

Time-Series Analysis and Forecasting

Additional Topics in Sampling

Filters

The two regressions Y = β₀ + β₁X₁ + β₂X₂ + β₃X₃ + β₄X₄ + ε and Y = β₀ + β₁X₁ + β₂X₂ + ε were run using a sample of 60 observations.If the SSE for the first regression is 1,688.4,what would you expect the SSE for the second regression be?

The adjusted coefficient of determination, ²,compared to R²,provides a better comparison between multiple regression models with different numbers of independent variables.

The multiple coefficient of determination R² can only be used to compare regression models that have the same set of sample observations of y_i,where i =1,2,…,n.

In multiple regression,to test H₀ : β₁= β₂ = ∙ ∙ ∙ ∙ ∙ ∙ = β_k= 0,a t-statistic with n - K degrees of freedom is used.

The manager's null and alternative hypotheses for β₁is: