Hockey Teams An avid hockey fan was in the process of examining the factors that determine the success or failure of hockey teams.He noticed that teams with many rookies and teams with many veterans seem to do quite poorly.To further analyze his beliefs he took a random sample of 20 teams and proposed a second-order model with one independent variable,average years of professional experience.The selected model is y = βS1U1B10S1U1B0 + βS1U1B11S1U1B0x + βS1U1B12S1U1B0xS1U1P12S1S1P0 + ε,where y = winning team's percentage,and x = average years of professional experience.The computer output is shown below. THE REGRESSION EQUATION IS y = 32.6 + 5.96x− .48xS1U1P12S1S1P0 S = 16.1 R−Sq = 43.9% ANALYSIS OF VARIANCE -{Hockey Teams Narrative} What is the coefficient of determination? Explain what this statistic tells you about the model.

R 2 = .439,which means that 43.9

For the following regression equation ,a unit increase in x2 increases the value of y on average by:

A) 4 B) 7 C) 17 D) an amount that depends on the value of x1. A) 4 B) 7 C) 17 D) an amount that depends on the value of x1.

Incomes of Physicians An economist is analyzing the incomes of physicians (general practitioners,surgeons,and psychiatrists).He realizes that an important factor is the number of years of experience.However,he wants to know if there are differences among the three professional groups.He takes a random sample of 125 physicians and estimates the multiple regression model y = βS1U1B10S1U1B0 + βS1U1B11S1U1B0xS1U1B11S1U1B0 + βS1U1B12S1U1B0xS1U1B12S1U1B0 + βS1U1B13S1U1B0xS1U1B13S1U1B0 + ε,where y = annual income (in $1,000),xS1U1B11S1U1B0 = years of experience,xS1U1B12S1U1B0 = 1 if physician and 0 if not,and xS1U1B13S1U1B0 = 1 if surgeons and 0 if not.The computer output is shown below. THE REGRESSION EQUATION IS y = 71.65 + 2.07xS1U1B11S1U1B0 + 10.16xS1U1B12S1U1B0− 7.44xS1U1B13S1U1B0 S = 42.6 R−Sq = 30.9% ANALYSIS OF VARIANCE -{Incomes of Physicians Narrative} Is there enough evidence at the 5% significance level to conclude that income and experience are linearly related?

H 0 : β 1 = 0 vs.H 1 : β 1 ≠ 0 Rejection region: |

Silver Prices An economist is in the process of developing a model to predict the price of silver.She believes that the two most important variables are the price of a barrel of oil (xS1U1B11S1U1B0)and the interest rate (xS1U1B12S1U1B0).She proposes the first-order model with interaction: y = βS1U1B10S1U1B0 + βS1U1B11S1U1B0xS1U1B11S1U1B0 + βS1U1B12S1U1B0xS1U1B12S1U1B0 + βS1U1B13S1U1B0xS1U1B11S1U1B0xS1U1B13S1U1B0 + ε.A random sample of 20 daily observations was taken.The computer output is shown below. THE REGRESSION EQUATION IS y = 115.6 + 22.3xS1U1B11S1U1B0 + 14.7xS1U1B12S1U1B0− 1.36xS1U1B11S1U1B0xS1U1B12S1U1B0 S = 20.9 R−Sq = 55.4% ANALYSIS OF VARIANCE -{Silver Prices Narrative} Do these results allow us at the 5% significance level to conclude that the model is useful in predicting the price of silver?

H 0 : β 1 = β 2 = β 3 = 0,H 1 : At least one β i is no

Motorcycle Fatalities A traffic consultant has analyzed the factors that affect the number of motorcycle fatalities.She has come to the conclusion that two important variables are the number of motorcycle and the number of cars.She proposed the model (the second-order model with interaction),where y = number of annual fatalities per county,xS1U1B11S1U1B0 = number of motorcycles registered in the county (in 10,000),and xS1U1B12S1U1B0 = number of cars registered in the county (in 1000).The computer output (based on a random sample of 35 counties)is shown below: THE REGRESSION EQUATION IS S = 15.2 R−Sq = 47.2% ANALYSIS OF VARIANCE -{Motorcycle Fatalities Narrative} Test at the 1% significance level to determine if the x2 term should be retained in the model.

H 0 : β 2 = 0 vs.H 1 : β 2 ≠ 0 Rejection region: |

Hockey Teams An avid hockey fan was in the process of examining the factors that determine the success or failure of hockey teams.He noticed that teams with many rookies and teams with many veterans seem to do quite poorly.To further analyze his beliefs he took a random sample of 20 teams and proposed a second-order model with one independent variable,average years of professional experience.The selected model is y = βS1U1B10S1U1B0 + βS1U1B11S1U1B0x + βS1U1B12S1U1B0xS1U1P12S1S1P0 + ε,where y = winning team's percentage,and x = average years of professional experience.The computer output is shown below. THE REGRESSION EQUATION IS y = 32.6 + 5.96x− .48xS1U1P12S1S1P0 S = 16.1 R−Sq = 43.9% ANALYSIS OF VARIANCE -{Hockey Teams Narrative} Test to determine at the 10% significance level if the linear term should be retained.

H 0 : β 1 = 0 vs.H 1 : β 1 ≠ 0 Rejection

Exam 18: Model Building

To gather the required observations for your potential regression models,a general rule is that there should be at least ____________________ observations for each independent variable used in the equation.

(Short Answer)

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Question 41

In explaining the amount of money spent on gifts for a child's birthday each year,the independent variable,age of child,is best represented by a dummy variable.

(True/False)

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Question 42

The model is referred to as a polynomial model with one predictor variable.

(True/False)

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Question 43

Computer Training Consider the following data for two variables,x and y.The independent variable x represents the amount of training time (in hours)for a salesperson starting in a new computer store to adjust fully,and the dependent variable y represents the weekly sales (in $1000s). Use statistical software to answer the following question(s). -{Computer Training Narrative} Develop an estimated regression equation of the form .

(Essay)

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Question 44

In regression analysis,a nominal independent variable such as color,with three different categories such as red,white,and blue,is best represented by three indicator variables to represent the three colors.

(True/False)

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Question 45

Hockey Teams An avid hockey fan was in the process of examining the factors that determine the success or failure of hockey teams.He noticed that teams with many rookies and teams with many veterans seem to do quite poorly.To further analyze his beliefs he took a random sample of 20 teams and proposed a second-order model with one independent variable,average years of professional experience.The selected model is y = β₀ + β₁x + β₂x² + ε,where y = winning team's percentage,and x = average years of professional experience.The computer output is shown below. THE REGRESSION EQUATION IS y = 32.6 + 5.96x− .48x² S = 16.1 R−Sq = 43.9% ANALYSIS OF VARIANCE -{Hockey Teams Narrative} What is the coefficient of determination? Explain what this statistic tells you about the model.

(Essay)

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Question 46

For the following regression equation ,a unit increase in x₂ increases the value of y on average by:

(Multiple Choice)

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Question 47

Suppose that the sample regression equation of a model is .If we examine the relationship between x₁ and y for four different values of x₂,we observe that the four equations produced differ only in the intercept term.

(True/False)

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Question 48

In order to represent 3 categories of a nominal variable,we need to create _______________ indicator variables.

(Short Answer)

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Question 49

Discuss briefly the procedure that is employed in the building of a model.

(Essay)

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Question 50

In a first-order polynomial model with no interaction,the effect of x₁ on y remains the same no matter what the value of x₂ is.The graph of this model produces straight lines that are ____________________ to each other.

(Short Answer)

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Question 51

An indicator variable is also called:

(Multiple Choice)

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Question 52

Incomes of Physicians An economist is analyzing the incomes of physicians (general practitioners,surgeons,and psychiatrists).He realizes that an important factor is the number of years of experience.However,he wants to know if there are differences among the three professional groups.He takes a random sample of 125 physicians and estimates the multiple regression model y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε,where y = annual income (in $1,000),x₁ = years of experience,x₂ = 1 if physician and 0 if not,and x₃ = 1 if surgeons and 0 if not.The computer output is shown below. THE REGRESSION EQUATION IS y = 71.65 + 2.07x₁ + 10.16x₂− 7.44x₃ S = 42.6 R−Sq = 30.9% ANALYSIS OF VARIANCE -{Incomes of Physicians Narrative} Is there enough evidence at the 5% significance level to conclude that income and experience are linearly related?

(Essay)

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Question 53

The model is referred to as a simple linear regression model.

(True/False)

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Question 54

Silver Prices An economist is in the process of developing a model to predict the price of silver.She believes that the two most important variables are the price of a barrel of oil (x₁)and the interest rate (x₂).She proposes the first-order model with interaction: y = β₀ + β₁x₁ + β₂x₂ + β₃x₁x₃ + ε.A random sample of 20 daily observations was taken.The computer output is shown below. THE REGRESSION EQUATION IS y = 115.6 + 22.3x₁ + 14.7x₂− 1.36x₁x₂ S = 20.9 R−Sq = 55.4% ANALYSIS OF VARIANCE -{Silver Prices Narrative} Do these results allow us at the 5% significance level to conclude that the model is useful in predicting the price of silver?

(Essay)

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Question 55

Motorcycle Fatalities A traffic consultant has analyzed the factors that affect the number of motorcycle fatalities.She has come to the conclusion that two important variables are the number of motorcycle and the number of cars.She proposed the model (the second-order model with interaction),where y = number of annual fatalities per county,x₁ = number of motorcycles registered in the county (in 10,000),and x₂ = number of cars registered in the county (in 1000).The computer output (based on a random sample of 35 counties)is shown below: THE REGRESSION EQUATION IS S = 15.2 R−Sq = 47.2% ANALYSIS OF VARIANCE -{Motorcycle Fatalities Narrative} Test at the 1% significance level to determine if the x₂ term should be retained in the model.

(Essay)

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Question 56

Hockey Teams An avid hockey fan was in the process of examining the factors that determine the success or failure of hockey teams.He noticed that teams with many rookies and teams with many veterans seem to do quite poorly.To further analyze his beliefs he took a random sample of 20 teams and proposed a second-order model with one independent variable,average years of professional experience.The selected model is y = β₀ + β₁x + β₂x² + ε,where y = winning team's percentage,and x = average years of professional experience.The computer output is shown below. THE REGRESSION EQUATION IS y = 32.6 + 5.96x− .48x² S = 16.1 R−Sq = 43.9% ANALYSIS OF VARIANCE -{Hockey Teams Narrative} Test to determine at the 10% significance level if the linear term should be retained.

(Essay)

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Question 57

The stepwise regression procedure begins by computing the simple regression model for each independent variable.

(True/False)

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Question 58

Indicator variables can assume as many values as there are categories of its corresponding nominal variable.

(True/False)

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Question 59

When the dependent variable is nominal,a(n)____________________ regression model is used.

(Short Answer)

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Question 60

Showing 41 - 60 of 148

To gather the required observations for your potential regression models,a general rule is that there should be at least ____________________ observations for each independent variable used in the equation.

In explaining the amount of money spent on gifts for a child's birthday each year,the independent variable,age of child,is best represented by a dummy variable.

The model is referred to as a polynomial model with one predictor variable.

In regression analysis,a nominal independent variable such as color,with three different categories such as red,white,and blue,is best represented by three indicator variables to represent the three colors.

For the following regression equation ,a unit increase in x₂ increases the value of y on average by:

Suppose that the sample regression equation of a model is .If we examine the relationship between x₁ and y for four different values of x₂,we observe that the four equations produced differ only in the intercept term.

In order to represent 3 categories of a nominal variable,we need to create _______________ indicator variables.

Discuss briefly the procedure that is employed in the building of a model.

In a first-order polynomial model with no interaction,the effect of x₁ on y remains the same no matter what the value of x₂ is.The graph of this model produces straight lines that are ____________________ to each other.

An indicator variable is also called:

The model is referred to as a simple linear regression model.

The stepwise regression procedure begins by computing the simple regression model for each independent variable.

Indicator variables can assume as many values as there are categories of its corresponding nominal variable.

When the dependent variable is nominal,a(n)____________________ regression model is used.

What Is Statistics

Graphical Descriptive Techniques 1

Graphical Descriptive Techniques 2

Numerical Descriptive Techniques

Data Collection and Sampling

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Introduction to Estimation

Introduction to Hypothesis Testing

Inference About a Population

Inference About Comparing Two Populations

Analysis of Variance

Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Nonparametric Statistics

Time-Series Analytics and Forecasting

Statistical Process Control

Decision Analysis

Conclusion

Filters

Exam 18: Model Building

To gather the required observations for your potential regression models,a general rule is that there should be at least ____________________ observations for each independent variable used in the equation.

In explaining the amount of money spent on gifts for a child's birthday each year,the independent variable,age of child,is best represented by a dummy variable.

The model is referred to as a polynomial model with one predictor variable.

In regression analysis,a nominal independent variable such as color,with three different categories such as red,white,and blue,is best represented by three indicator variables to represent the three colors.

For the following regression equation ,a unit increase in x2 increases the value of y on average by:

Suppose that the sample regression equation of a model is .If we examine the relationship between x1 and y for four different values of x2,we observe that the four equations produced differ only in the intercept term.

In order to represent 3 categories of a nominal variable,we need to create _______________ indicator variables.

Discuss briefly the procedure that is employed in the building of a model.

In a first-order polynomial model with no interaction,the effect of x1 on y remains the same no matter what the value of x2 is.The graph of this model produces straight lines that are ____________________ to each other.

An indicator variable is also called:

The model is referred to as a simple linear regression model.

The stepwise regression procedure begins by computing the simple regression model for each independent variable.

Indicator variables can assume as many values as there are categories of its corresponding nominal variable.

When the dependent variable is nominal,a(n)____________________ regression model is used.

What Is Statistics

Graphical Descriptive Techniques 1

Graphical Descriptive Techniques 2

Numerical Descriptive Techniques

Data Collection and Sampling

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Introduction to Estimation

Introduction to Hypothesis Testing

Inference About a Population

Inference About Comparing Two Populations

Analysis of Variance

Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Nonparametric Statistics

Time-Series Analytics and Forecasting

Statistical Process Control

Decision Analysis

Conclusion

Filters

For the following regression equation ,a unit increase in x₂ increases the value of y on average by:

Suppose that the sample regression equation of a model is .If we examine the relationship between x₁ and y for four different values of x₂,we observe that the four equations produced differ only in the intercept term.

In a first-order polynomial model with no interaction,the effect of x₁ on y remains the same no matter what the value of x₂ is.The graph of this model produces straight lines that are ____________________ to each other.