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 5% significance level to infer that the cholesterol level and the age at death show a negative linear relationship?

H 0 : β 2 = 0 against H 1 : β 2 < 0 Rejection regi

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 b3.

For every additional person in the house

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: In examining the determinants of income,data were collected regarding the characteristics of 45 adults,and the regression Y = βS1U1B10S1U1B0 + βS1U1B11S1U1B0XS1U1B11S1U1B0 + βS1U1B12S1U1B0XS1U1B12S1U1B0 + βS1U1B13S1U1B0XS1U1B13S1U1B0 +ε was used,where Y is the annual income (in thousands of dollars),XS1U1B11S1U1B0 is the person's age,XS1U1B12S1U1B0 is his/her years of education,and XS1U1B13S1U1B0 is a dummy variable = 1 if the adult is female. -If you get = 26.3 + 1.38x1 + 2.98x2 - 0.76x3 + 0.34(x2 ∙ x3)when you run the regression,how would you interpret the coefficient on his/her years of education?

A) For each additional year of education,women on average earn $420 less than men. B) For each additional year of education,women approximately earn $1,100 less than men. C) For each additional year of education,women on average earn an additional $3,320. D) For each additional year of education,women approximately earn $340 less than men. A) For each additional year of education,women on average earn $420 less than men. B) For each additional year of education,women approximately earn $1,100 less than men. C) For each additional year of education,women on average earn an additional $3,320. D) For each additional year of education,women approximately earn $340 less than men.

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 : β4 = 0 and interpret your result.

t = @#IMG-DLM& (j = 1,2,... ,K) t = @#IMG-DLM& = 0.46 Sinc

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. -The director of a local tourist board is interested in determining the factors that influence the hotel occupancy rate in his city each month.Hotel occupancy can be measured as the percentage of available hotel rooms that are occupied by paying customers.He develops two models: Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + ε and Y = β0 + β1X1 + β2X2 + ε,where Y is the hotel occupancy rate (as a percentage),X1 is the total number of passengers arriving at the airport (measured in thousands),X2 is an average of local hotel room rates,X3 is the consumer confidence index,and X4 is a dummy variable = 1 during the months of June,July and August.He looks at data from the past 36 months and runs both of the regressions above.The results of these regressions are as follows: Model 1: R2 = 0.67 and SSE = 576,Model 2: R2 = 0.61 and SSE = 733.Using the F- test on a subset of variables,test whether β3 = β4 = 0.

F = @#IMG-DLM& = @#IMG-DLM& = 4.22 Since F = 4.22,we can r

Exam 12: Multiple Regression

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 = β₀ + β₁X₁ + β₂X₂ + β₃X₃ + β₄X₄ + ε,where Y is the hotel occupancy rate,X₁ is the total number of passengers arriving at the airport,X₂ is a price index of local hotel room rates,X₃ is the consumer confidence index,and X₄ 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 + 0.02x₁ - 0.055x₂ + 0.08x₃ + 12.3x₄,R² = 0.67, = 58.3, = 0.008, = 0.01, = 0.06, = 4.7,and SSE = 576. -Interpret the estimated regression coefficient b₃.

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Question 181

To test the validity of a multiple regression model involving three independent variables,the null hypothesis states that:

(Multiple Choice)

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Question 182

What factors would tend to increase the difference between the coefficient of determination R² and the adjusted R² for a multiple regression?

(Short Answer)

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Question 183

The coefficients from a regression using the exponential model transformation may be interpreted as elasticities.

(True/False)

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Question 184

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 b₂.

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Question 185

The interpretation of the slope is exactly the same in a multiple linear regression model as compared to a simple linear regression model.

(True/False)

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Question 186

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 (x₁),the cholesterol level (x₂),and the number of points that the individual's blood pressure exceeded the recommended value (x₃).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 + 1.79x₁ - 0.021x₂ - 0.016x₃ S = 9.47 R-Sq = 22.5% ANALYSIS OF VARIANCE -Is there enough evidence at the 5% significance level to infer that the cholesterol level and the age at death show a negative linear relationship?

(Essay)

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Question 187

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The director of a local tourist board is interested in determining the factors that influence the hotel occupancy rate in his city each month.Hotel occupancy can be measured as the percentage of available hotel rooms that are occupied by paying customers.He develops the model: lnY = β₀+ β₁lnX₁ + β₂lnX₂ + β₃lnX₃ + β₄X₄+ ε,where Y is the hotel occupancy rate (as a percentage),X₁ is the total number of passengers arriving at the airport (measured in thousands),X₂ is an average of local hotel room rates,X₃ is the consumer confidence index,and X₄ is a dummy variable = 1 during the months of June,July,and August.He looks at the data from the past 36 months and obtains ln = 4.2 + 1.23lnx₁ - 2.2lnx₂ + 0.34ln x₃+ 2.3x₄ and R² = 0.63. -What would you forecast the occupancy rate to be this July when we expect 525,000 visitors? We would anticipate the room rate to average $130 and consumer confidence to be 110.

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Question 188

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: In examining the determinants of income,data were collected regarding the characteristics of 45 adults,and the regression lnY = β₀+ β₁lnX₁ + β₂ lnX₂ + β₃X₃ + ε was used,where Y is the annual income (in thousands of dollars),X₁ is the adult's age,X₂ is his/her years of education,and X₃ is a dummy variable = 1 and is used if the adult is female.You run the regression and obtain the equation ln = 6.3 + 0.91 lnx₁ + 1.3 ln x₂ - 0.05x₃. -How would you interpret the coefficient on years of education?

(Multiple Choice)

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Question 189

We would always use a quadratic term in a regression when we think there is a nonlinear relationship between the dependent and independent variable.

(True/False)

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Question 190

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The computer output for the multiple regression model,y = β₀ + β₁X₁ + β₂X₂ + ε is shown below.However,because of a printer malfunction some of the results are not shown.These are identified by asterisks. S = * R-Sq = * ANALYSIS OF VARIANCE -If you want to test H₀ : β₁ = β₂ = 0 against H₁ : At least one β_j ≠ 0,(j = 1,2),what is the test statistic? What is your conclusion at the 5% level?

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Question 191

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 = β₀ + β₁X₁ + β₂X₂ + β₃X₃ + β₄X₄ + ε,where Y is the amount of time (in minutes),X₁ is the income of the individual (in thousands of dollars),X₂ is the age of the individual,X₃ is the number of people living in the household,and X₄ 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 + 3.8x₁ - 1.04x₂ + 2.15x₃ + 15.1x₄, = 5.3, = 0.13, = 0.33, = 1.51, = 4.7,SSR = 164.2,SSE = 200.7,and R² = 0.45. -Interpret the estimated regression coefficient b₃.

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Question 192

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 (x₁),the cholesterol level (x₂),and the number of points that the individual's blood pressure exceeded the recommended value (x₃).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 + 1.79x₁ - 0.021x₂ - 0.016x₃ S = 9.47 R-Sq = 22.5% ANALYSIS OF VARIANCE -Interpret the coefficient b₂.

(Essay)

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Question 193

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: In examining the determinants of income,data were collected regarding the characteristics of 45 adults,and the regression Y = β₀ + β₁X₁ + β₂X₂ + β₃X₃ +ε was used,where Y is the annual income (in thousands of dollars),X₁ is the person's age,X₂ is his/her years of education,and X₃ is a dummy variable = 1 if the adult is female. -If you get = 26.3 + 1.38x₁ + 2.98x₂ - 0.76x₃+ 0.34(x₂ ∙ x₃)when you run the regression,how would you interpret the coefficient on his/her years of education?

(Multiple Choice)

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Question 194

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 = β₀ + β₁X₁ + β₂X₂ + β₃ + β₄X₃ + β₅X₄+ β₆(X₁ ∙ X₄)+ ε,where Y is the amount of time in minutes,X₁ is the income of the individual (in thousands of dollars),X₂ is the age of the individual,X₃ is the number of people living in the household,and X₄ 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 + 0.38x₁ + 1.04x₂ - 0.04 + 2.15x₃ + 0.11x₄ - 0.22(x₁ ∙ x₄), = 5.3, = 0.13, = 0.33, = 1.51, = 4.7, = 0.05,and = 0.07. -Test the hypothesis H₀: β₄= 0 and interpret your result.

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Question 195

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.The officer used lnY = β₀ + β₁lnX₁ + β₂lnX₂ + β₃lnX₃ + lnε to model the relationship,where Y is the total dollar value of residential loans in a month (in millions of dollars),X₁is the number of loans,X₂is the interest rate,and X₃is the dollar value of expenditures of the bank on advertising (in thousands of dollars).Using data from the past 24 months,she obtained ln = 0.67 + 1.2 ln x₁ - 1.45 ln x₂ + 1.07 ln x₃. -How would the officer interpret the coefficient on x₂?

(Multiple Choice)

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Question 196

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.The officer used lnY = β₀ + β₁lnX₁ + β₂lnX₂ + β₃lnX₃ + lnε to model the relationship,where Y is the total dollar value of residential loans in a month (in millions of dollars),X₁is the number of loans,X₂is the interest rate,and X₃is the dollar value of expenditures of the bank on advertising (in thousands of dollars).Using data from the past 24 months,she obtained ln = 0.67 + 1.2 ln x₁ - 1.45 ln x₂ + 1.07 ln x₃. -How would the officer interpret the coefficient on x₃?

(Multiple Choice)

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Question 197

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 = β₀ + β₁X₁ + β₂X₂ + β₃X₃ + β₄X₄ + ε,where Y is the hotel occupancy rate,X₁ is the total number of passengers arriving at the airport,X₂ is a price index of local hotel room rates,X₃ is the consumer confidence index,and X₄ 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 + 0.02x₁ - 0.055x₂ + 0.08x₃ + 12.3x₄,R² = 0.67, = 58.3, = 0.008, = 0.01, = 0.06, = 4.7,and SSE = 576. -The director of a local tourist board is interested in determining the factors that influence the hotel occupancy rate in his city each month.Hotel occupancy can be measured as the percentage of available hotel rooms that are occupied by paying customers.He develops two models: Y = β₀ + β₁X₁ + β₂X₂ + β₃X₃ + β₄X₄ + ε and Y = β₀ + β₁X₁ + β₂X₂ + ε,where Y is the hotel occupancy rate (as a percentage),X₁ is the total number of passengers arriving at the airport (measured in thousands),X₂ is an average of local hotel room rates,X₃ is the consumer confidence index,and X₄ is a dummy variable = 1 during the months of June,July and August.He looks at data from the past 36 months and runs both of the regressions above.The results of these regressions are as follows: Model 1: R² = 0.67 and SSE = 576,Model 2: R²= 0.61 and SSE = 733.Using the F- test on a subset of variables,test whether β₃= β₄ = 0.

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Question 198

In order to test the significance of a multiple regression model involving 5 independent variables and 50 observations,the numerator and denominator degrees of freedom for the critical value of F are 5 and 45 respectively.

(True/False)

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Question 199

In multiple regression analysis,the ratio MSR/ yields the:

(Multiple Choice)

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Question 200

Showing 181 - 200 of 252

To test the validity of a multiple regression model involving three independent variables,the null hypothesis states that:

What factors would tend to increase the difference between the coefficient of determination R² and the adjusted R² for a multiple regression?

The coefficients from a regression using the exponential model transformation may be interpreted as elasticities.

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 b₂.

The interpretation of the slope is exactly the same in a multiple linear regression model as compared to a simple linear regression model.

We would always use a quadratic term in a regression when we think there is a nonlinear relationship between the dependent and independent variable.

In order to test the significance of a multiple regression model involving 5 independent variables and 50 observations,the numerator and denominator degrees of freedom for the critical value of F are 5 and 45 respectively.

In multiple regression analysis,the ratio MSR/ yields the:

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

To test the validity of a multiple regression model involving three independent variables,the null hypothesis states that:

What factors would tend to increase the difference between the coefficient of determination R2 and the adjusted R2 for a multiple regression?

The coefficients from a regression using the exponential model transformation may be interpreted as elasticities.

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 b2.

The interpretation of the slope is exactly the same in a multiple linear regression model as compared to a simple linear regression model.

We would always use a quadratic term in a regression when we think there is a nonlinear relationship between the dependent and independent variable.

In order to test the significance of a multiple regression model involving 5 independent variables and 50 observations,the numerator and denominator degrees of freedom for the critical value of F are 5 and 45 respectively.

In multiple regression analysis,the ratio MSR/ yields the:

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

What factors would tend to increase the difference between the coefficient of determination R² and the adjusted R² for a multiple regression?

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 b₂.