Question 1

A multiple regression model has the form   = 8 + 3x1 + 5x2 4x3.As x3 increases by one unit,with x1 and x2 held constant,then y,on average,is expected to:

Accepted Answer

A) increase by 1 unit. 
B) decrease by 4 units. 
C) increase by 12 units. 
D) decrease by 16 units. 
A) increase by 1 unit. 
B) decrease by 4 units. 
C) increase by 12 units. 
D) decrease by 16 units.

Question 2

What can the manager infer about the relationship between the square of the level of output and the average costs?

Accepted Answer

A) As the level of output increases,average costs decrease at an increasing rate. 
B) As the level of output increases,at first average costs decrease,then will start to increase. 
C) As the level of output increases,at first average costs increase,then will start to decrease. 
D) As the level of output increases,average costs increase at an increasing rate. 
A) As the level of output increases,average costs decrease at an increasing rate. 
B) As the level of output increases,at first average costs decrease,then will start to increase. 
C) As the level of output increases,at first average costs increase,then will start to decrease. 
D) As the level of output increases,average costs increase at an increasing rate.

Question 3

What is the value of se?

Accepted Answer

A) 0.042 
B) 0.82 
C) 0.73 
D) 0.0018 
A) 0.042 
B) 0.82 
C) 0.73 
D) 0.0018

Question 4

Determine the profit for the 11 year,if the revenue per deposit dollar and offices are 3.82 and 6,358 respectively.

Accepted Answer

A) 0.82 
B) 6.86 
C) 0.79 
D) 8.16 
A) 0.82 
B) 6.86 
C) 0.79 
D) 8.16

Question 5

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
For the regression model   
S1U1B1iS1U1B0S1U1B1 S1U1B0= bS1U1B10S1U1B0 + bS1U1B11S1U1B0xS1U1B11S1U1B0S1U1B1iS1U1B0 + bS1U1B12S1U1B0xS1U1B12S1U1B0S1U1B1iS1U1B0,the following summary statistics are given:
r   
S1U1B1yS1U1B0 = 0.58;r   
S1U1B1y S1U1B0= -0.50;r   
   
= -0.58;s   
S1U1B1 S1U1B0= 180;s   
S1U1B1 S1U1B0= 90;andS1U1B1 S1U1B0sS1U1B1yS1U1B0 = 360.
-Compute the coefficient b1.

Accepted Answer

b₁ = @#IMG-DLM& = @#IMG-DLM&

Question 6

What would we expect the total dollar value of loans to be in a month where there are 42 loans,the interest rate is 7.5%,and the bank spends $30,000 in advertising?

Accepted Answer

A) $6.442 million 
B) $6.558 million 
C) $6.288 million 
D) $6.112 million 
A) $6.442 million 
B) $6.558 million 
C) $6.288 million 
D) $6.112 million

Question 7

In a multiple regression model,which of the following is true of the value of R2 adjusted for the degrees of freedom?

Accepted Answer

A) It can be negative. 
B) It has to be positive. 
C) It has to be larger than the multiple coefficient of determination. 
D) It can be larger than 1. 
A) It can be negative. 
B) It has to be positive. 
C) It has to be larger than the multiple coefficient of determination. 
D) It can be larger than 1.

Question 8

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
In a study of foreign holdings in Egyptian banks,the following sample regression results were obtained,based on 14 annual observations:   
= -3.25 +   
-   
+   
,and RS1U1P12S1S1P0S1U1P1 S1S1P0= 0.92,
Where the numbers in parentheses under the coefficient estimates are the estimated coefficient standard errors,and
y = Year-end share of assets in Egyptian bank subsidiaries held by foreigners,as a percentage of total assets
xS1U1B11S1U1B0 = Annual change,in billions of Egyptian pounds,in foreign direct investment in Egypt
xS1U1B12S1U1B0 = Bank price-earnings ratio
xS1U1B13S1U1B0 = Index of the exchange value of the Egyptian pounds
-Test the null hypothesis that β3 is zero,against the alternative that it is positive at the 5% significance level,and interpret your result.

Accepted Answer

H₀ : β₃_{= 0,}H₁_:β₃_{> 0} Reject H₀if t > t_n-K_-1,α= t_10,0.05= 1.812 The t

Question 9

In a multiple regression problem involving two independent variables X1 and X2,what does it mean if the value of b1 is 3.2?

Accepted Answer

A) The relationship between X1 and Y is significant. 
B) The estimated value of Y increases by an average of 3.2 units for each unit increase of X1,holding X2 constant. 
C) The estimated value of Y increases approximately by 3.2 units for each unit increase of X2,holding X1 constant. 
D) The estimated average value of Y is 3.2 units when X1 = 0. 
A) The relationship between X1 and Y is significant. 
B) The estimated value of Y increases by an average of 3.2 units for each unit increase of X1,holding X2 constant. 
C) The estimated value of Y increases approximately by 3.2 units for each unit increase of X2,holding X1 constant. 
D) The estimated average value of Y is 3.2 units when X1 = 0.

Question 10

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A regression analysis has produced the following partial analysis of variance table:
Analysis of Variance
  
-Test H0 : β1 = β2 = β3 = β4 = 0 against H1 : At least one βj ≠ 0,(j = 1,2,3,4)at the 1% significance level.

Accepted Answer

Reject H₀if F > F_K,n-K-1,α.= F_4,30,0.01= 4.02. Si

Question 11

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A professor investigated some of the factors that affect an individual student's final grade in his course.He proposed the multiple regression model Y = βS1U1B10S1U1B0 + βS1U1B11S1U1B0XS1U1B11S1U1B0 + βS1U1B12S1U1B0XS1U1B12S1U1B0 + βS1U1B13S1U1B0XS1U1B13S1U1B0 + ε ,where Y is the final mark (out of 100),XS1U1B11S1U1B0 is the number of lectures skipped,XS1U1B12S1U1B0 is the number of late assignments,and XS1U1B13S1U1B0 is the mid-term test mark (out of 100).The professor recorded the data for 50 randomly selected students.The computer output is shown below.
The regression equation is   
= 41.6 - 3.18xS1U1B11S1U1B0 - 1.17xS1U1B12S1U1B0 + 0.63xS1U1B13S1U1B0.
   
S = 13.74 R-Sq = 30.0%
ANALYSIS OF VARIANCE
  
-What is the coefficient of determination? What does this statistic tell you?

Accepted Answer

The coefficient of determination is R² =

Question 12

What role does the adjusted coefficient of determination,   2,play in multiple regression analysis?

Accepted Answer

A) It tests the significance of all independent variables. 
B) It corrects the coefficient R2 for the number of independent variables. 
C) It helps detect nonsignificant predictor variables. 
D) It helps in the determination of the F-statistic for evaluating the overall statistical significance of the model. 
A) It tests the significance of all independent variables. 
B) It corrects the coefficient R2 for the number of independent variables. 
C) It helps detect nonsignificant predictor variables. 
D) It helps in the determination of the F-statistic for evaluating the overall statistical significance of the model.

Question 13

In testing the validity of a multiple regression model,a large value of the F-test statistic indicates that:

Accepted Answer

A) most of the variation in the independent variables is explained by the variation in y. 
B) the model has significant explanatory power because at least one slope coefficient is not zero. 
C) most of the variation in y is unexplained by the regression equation. 
D) the model provides a poor fit. 
A) most of the variation in the independent variables is explained by the variation in y. 
B) the model has significant explanatory power because at least one slope coefficient is not zero. 
C) most of the variation in y is unexplained by the regression equation. 
D) the model provides a poor fit.

Question 14

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 : β6 = 0 and interpret your result.

Accepted Answer

t = @#IMG-DLM& 
(j = 1,2,... ,K)
t = @#IMG-DLM& 
= -3.14
Sin

Question 15

Which of the following is the value of SSE?

Accepted Answer

A) 6.00 
B) 0.0018 
C) 0.011 
D) 9.26 
A) 6.00 
B) 0.0018 
C) 0.011 
D) 9.26

Question 16

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
As director of the local tourist board,you are interested in determining the factors that influence the hotel occupancy rate in your city each month.Hotel occupancy can be measured as the percentage of available hotel rooms that are occupied by paying customers.You develop the following model: Y = βS1U1B10S1U1B0 + βS1U1B11S1U1B0XS1U1B11S1U1B0 + βS1U1B12S1U1B0XS1U1B12S1U1B0 + βS1U1B13S1U1B0XS1U1B13S1U1B0 + βS1U1B14S1U1B0XS1U1B14S1U1B0 + ε,where Y is the hotel occupancy rate,XS1U1B11S1U1B0 is the total number of passengers arriving at the airport,XS1U1B12S1U1B0 is a price index of local hotel room rates,XS1U1B13S1U1B0 is the consumer confidence index,and XS1U1B14S1U1B0 is a dummy variable = 1 during the months of June,July,and August.You look at data from the past 36 months and obtain the following results:   
= 67.1 + 0.02xS1U1B11S1U1B0 - 0.055xS1U1B12S1U1B0 + 0.08xS1U1B13S1U1B0 + 12.3xS1U1B14S1U1B0,RS1U1P12S1S1P0 = 0.67,   
= 58.3,   
= 0.008,   
= 0.01,   
= 0.06,   
= 4.7,and SSE = 576.
-Test the hypothesis H0 : β4 = 0 and interpret your results.

Accepted Answer

t = @#IMG-DLM& 
(j = 1,2,... ,K)
t = @#IMG-DLM& 
= 2.62
Sinc

Question 17

In a multiple regression model,there are four independent variables and 60 observations.What are the degrees of freedom associated with the error sum of squares?

Accepted Answer

A) 56 
B) 4 
C) 55 
D) 3 
A) 56 
B) 4 
C) 55 
D) 3

Question 18

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.
-What are the model constant and the slope coefficient of x1 when x2 equals 1 in the equation   
?

Accepted Answer

Question 19

What is the most accurate conclusion regarding the hypothesis test for β2?

Accepted Answer

A) fail to reject H0 at α > 0.10 
B) reject H0 at all levels of α 
C) reject H00 only at α = 0.05 
D) fail to reject H0 at α = 0.005 
A) fail to reject H0 at α > 0.10 
B) reject H0 at all levels of α 
C) reject H00 only at α = 0.05 
D) fail to reject H0 at α = 0.005

Question 20

A multiple regression is called "multiple" because it has several explanatory variables.

Accepted Answer

A) True 
 B)False

A multiple regression model has the form = 8 + 3x₁ + 5x₂ 4x₃.As x₃ increases by one unit,with x₁ and x₂ held constant,then y,on average,is expected to:

What can the manager infer about the relationship between the square of the level of output and the average costs?

What is the value of s_e?

Determine the profit for the 11 year,if the revenue per deposit dollar and offices are 3.82 and 6,358 respectively.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: For the regression model _i= b₀ + b₁x₁_i + b₂x₂_i,the following summary statistics are given: r _y = 0.58;r _y= -0.50;r = -0.58;s = 180;s = 90;ands_y = 360. -Compute the coefficient b₁.

What would we expect the total dollar value of loans to be in a month where there are 42 loans,the interest rate is 7.5%,and the bank spends $30,000 in advertising?

In a multiple regression model,which of the following is true of the value of R² adjusted for the degrees of freedom?

In a multiple regression problem involving two independent variables X₁ and X₂,what does it mean if the value of b₁ is 3.2?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A regression analysis has produced the following partial analysis of variance table: Analysis of Variance -Test H₀ : β₁ = β₂ = β₃ = β₄= 0 against H₁_:At least one β_j≠ 0,(j = 1,2,3,4)at the 1% significance level.

What role does the adjusted coefficient of determination, ²,play in multiple regression analysis?

In testing the validity of a multiple regression model,a large value of the F-test statistic indicates that:

Which of the following is the value of SSE?

In a multiple regression model,there are four independent variables and 60 observations.What are the degrees of freedom associated with the error sum of squares?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Assume that x₁ is a continuous variable and x₂ is a dummy variable with a value of 0 or 1. -What are the model constant and the slope coefficient of x₁ when x₂equals 1 in the equation ?

What is the most accurate conclusion regarding the hypothesis test for β₂?

A multiple regression is called "multiple" because it has several explanatory variables.

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

Exam 12: Multiple Regression

A multiple regression model has the form = 8 + 3x1 + 5x2 4x3.As x3 increases by one unit,with x1 and x2 held constant,then y,on average,is expected to:

What can the manager infer about the relationship between the square of the level of output and the average costs?

What is the value of se?

Determine the profit for the 11 year,if the revenue per deposit dollar and offices are 3.82 and 6,358 respectively.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: For the regression model i = b0 + b1x1i + b2x2i,the following summary statistics are given: r y = 0.58;r y = -0.50;r = -0.58;s = 180;s = 90;and sy = 360. -Compute the coefficient b1.

What would we expect the total dollar value of loans to be in a month where there are 42 loans,the interest rate is 7.5%,and the bank spends $30,000 in advertising?

In a multiple regression model,which of the following is true of the value of R2 adjusted for the degrees of freedom?

In a multiple regression problem involving two independent variables X1 and X2,what does it mean if the value of b1 is 3.2?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A regression analysis has produced the following partial analysis of variance table: Analysis of Variance -Test H0 : β1 = β2 = β3 = β4 = 0 against H1 : At least one βj ≠ 0,(j = 1,2,3,4)at the 1% significance level.

What role does the adjusted coefficient of determination, 2,play in multiple regression analysis?

In testing the validity of a multiple regression model,a large value of the F-test statistic indicates that:

Which of the following is the value of SSE?

In a multiple regression model,there are four independent variables and 60 observations.What are the degrees of freedom associated with the error sum of squares?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Assume that x1 is a continuous variable and x2 is a dummy variable with a value of 0 or 1. -What are the model constant and the slope coefficient of x1 when x2 equals 1 in the equation ?

What is the most accurate conclusion regarding the hypothesis test for β2?

A multiple regression is called "multiple" because it has several explanatory variables.

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

A multiple regression model has the form = 8 + 3x₁ + 5x₂ 4x₃.As x₃ increases by one unit,with x₁ and x₂ held constant,then y,on average,is expected to:

What is the value of s_e?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: For the regression model _i= b₀ + b₁x₁_i + b₂x₂_i,the following summary statistics are given: r _y = 0.58;r _y= -0.50;r = -0.58;s = 180;s = 90;ands_y = 360. -Compute the coefficient b₁.

In a multiple regression model,which of the following is true of the value of R² adjusted for the degrees of freedom?

In a multiple regression problem involving two independent variables X₁ and X₂,what does it mean if the value of b₁ is 3.2?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A regression analysis has produced the following partial analysis of variance table: Analysis of Variance -Test H₀ : β₁ = β₂ = β₃ = β₄= 0 against H₁_:At least one β_j≠ 0,(j = 1,2,3,4)at the 1% significance level.

What role does the adjusted coefficient of determination, ²,play in multiple regression analysis?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Assume that x₁ is a continuous variable and x₂ is a dummy variable with a value of 0 or 1. -What are the model constant and the slope coefficient of x₁ when x₂equals 1 in the equation ?

What is the most accurate conclusion regarding the hypothesis test for β₂?