Deck 18: Model Building

Question 1

Suppose that the sample regression equation of a model is .If we examine the relationship between y and x₂ for x₁ = 1,2,and 3,we observe that the three equations produced not only differ in the intercept term,but the coefficient of x₂ also varies.

Answer 1

True

Question 2

In the first-order regression model ,a unit increase in x₁ increases the value of y on average by 6 units.

Answer 2

False

Question 3

In the first-order model ,a unit increase in x₂,while holding x₁ constant at a value of 3,decreases the value of y on average by 3 units.

Answer 3

False

Question 4

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

Question 5

Which of the following is not an advantage of multiple regression as compared with analysis of variance?

A)Multiple regression can be used to estimate the relationship between the dependent variable and independent variables.
B)Multiple regression handles problems with more than two independent variables easier than analysis of variance.
C)Multiple regression handles nominal variables better than analysis of variance.
D)All of these choices are true are advantages of multiple regression as compared with analysis of variance.

Question 6

The model y = β₀ + β₁x₁ + β₂x₂ + ε is referred to as a first-order model with two predictor variables with no interaction.

Question 7

The model is used whenever the statistician believes that,on average,y is linearly related to x₁ and x₂ and the predictor variables do not interact.

Question 8

Regression analysis allows the statistics practitioner to use mathematical models to realistically describe relationships between the dependent variable and independent variables.

Question 9

The graph of the model is shaped like a straight line going upwards.

Question 10

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.

Question 11

In a first-order model with two predictors x₁ and x₂,an interaction term may be used when the relationship between the dependent variable y and the predictor variables is linear.

Question 12

A first-order polynomial model with one predictor variable is the familiar simple linear regression model.

Question 13

In the first-order model ,a unit increase in x₂,while holding x₁ constant,increases the value of y on average by 5 units.

Question 14

We interpret the coefficients in a multiple regression model by holding all variables in the model constant.

Question 15

In the first-order model ,a unit increase in x₂,while holding x₁ constant at 1,changes the value of y on average by −5 units.

Question 16

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

Question 17

The model y = β₀ + β₁x₁ + β₂x₂ + β₃x₁x₂ + ε is referred to as a second-order model with two predictor variables with interaction.

Question 18

In a first-order model with two predictors x₁ and x₂,an interaction term may be used when the:

A)relationship between the dependent variable and the independent variables is linear.
B)effect of x₁ on the dependent variable is influenced by x₂.
C)Effect of x₂ on the dependent variable is influenced by x₁.
D) both b and c.

Question 19

Suppose that the sample regression line of the first-order model is .If we examine the relationship between y and x₁ for three different values of x₂,we observe that the effect of x₁ on y remains the same no matter what the value of x₂.

Question 20

In the first-order model ,a unit increase in x₁,while holding x₂ constant at a value of 2,decreases the value of y on average by 8 units.

Question 21

When we plot x versus y,the graph of the model y = β₀ + β₁x + β₂x² + ε is shaped like a:

A)straight line going upwards.
B)circle.
C)parabola.
D)None of these choices.

Question 22

The model y = β₀ + β₁x₁ + β₂x₂ + β₃x₁x₂ + ε is referred to as a:

A)first-order model with two predictor variables with no interaction.
B)first-order model with two predictor variables with interaction.
C)second-order model with three predictor variables with no interaction.
D)second-order model with three predictor variables with interaction.

Question 23

The model y = β₀ + β₁x₁ + β₂x₂ + ε is used whenever the statistician believes that,on average,y is linearly related to:

A)x₁ and the predictor variables do not interact.
B) x₂ and the predictor variables do not interact.
C) Both a and b.
D) None of these choices.

Question 24

Suppose that the sample regression equation of a second-order model is given by .Then,the value 4.60 is the:

A)predicted value of y for any positive value of x.
B)predicted value of y when x = 2.
C)estimated change in y when x increases by 1 unit .
D)intercept where the response surface strikes the x-axis.

Question 25

The independent variable x in a polynomial model is called the ____________________ variable.

Question 26

The model y = β₀ + β₁x + β₂x² + ε is referred to as a:

A)simple linear regression model.
B)first-order model with one predictor variable.
C)second-order model with one predictor variable.
D)third order model with two predictor variables.

Question 27

Suppose that the sample regression equation of a second-order model is given by .Then,the value 2.50 is the:

A)intercept where the response surface strikes the y-axis.
B)intercept where the response surface strikes the x-axis.
C)predicted value of y.
D)None of these choices.

Question 28

For the following regression equation ,a unit increase in x₁,while holding x₂ constant at a value of 2,decreases the value of y on average by:

A)92
B)85
C)20
D)an amount that depends on the value of x₁.

Question 29

The model y = β₀ + β₁x + β₂x² +.........+ β_px^p + ε is referred to as a polynomial model with:

A)one predictor variable.
B)p predictor variables.
C)(p + 1)predictor variables.
D)x predictor variables.

Question 30

For the following regression equation ,a unit increase in x₂,while holding x₁ constant at a value of 3,decreases the value of y on average by:

A)22
B)50
C)56
D)An amount that depends on the value of x₂

Question 31

The model y = β₀ + β₁x₁ + β₂x₂ + ε is referred to as a:

A)first-order model with one predictor variable.
B)first-order model with two predictor variables.
C)second-order model with one predictor variable.
D)second-order model with two predictor variables.

Question 32

For the following regression equation ,which combination of x₁ and x₂,respectively,results in the largest average value of y?

A)3 and 5
B)5 and 3
C)6 and 3
D)3 and 6

Question 33

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.

Question 34

For the following regression equation ,a unit increase in x₁ increases the value of y on average by:

A)5
B)30
C)26
D)an amount that depends on the value of x₂

Question 35

For the following regression equation ,a unit increase in x₂,while holding x₁ constant at 1,changes the value of y on average by:

A)−5
B)+5
C)10
D)−10

Question 36

Which of the following statements is false regarding the graph of the second-order polynomial model y = β₀ + β₁x + β₂x² + ε?

A)If β₂ is negative,the graph is concave,while if β₂ is positive,the graph is convex.
B)The greater the absolute value of β₂,the smaller the rate of curvature.
C)When we plot x versus y,the graph is shaped like a parabola.
D)All of these choices are true.

Question 37

Suppose that the sample regression line of the first-order model is .If we examine the relationship between y and x₁ for four different values of x₂,we observe that the:

A)only difference in the four equations produced is the coefficient of x₂.
B)effect of x₁ on y remains the same no matter what the value of x₂.
C)effect of x₁ on y remains the same no matter what the value of x₁.
D)Cannot answer this question without more information.

Question 38

Another term for a first-order polynomial model is a regression ____________________.

Question 39

A second-order polynomial model is shaped like a(n)____________________.

Question 40

Suppose that the sample regression equation of a model is .If we examine the relationship between x₁ and y for three different values of x₂,we observe that the:

A)three equations produced differ not only in the intercept term but also the coefficient of x₁ varies.
B)coefficient of x₂ remains unchanged.
C)coefficient of x₁ varies.
D)three equations produced differ only in the intercept.

Question 41

The model y = β₀ + β₁x₁ + β₂x₂ + β₃x₁x₂ + ε is a(n)____________________-order polynomial model with ____________________ predictor variables and ____________________.

Question 42

____________________ means that the effect of x₁ on y is influenced by the value of x₂,and vice versa.

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} Estimate the value of y when x = 45 using the estimated linear regression equation in the previous question.

Question 44

The model y = β₀ + β₁x₁ + β₂x₂ + ε is a(n)____________________-order polynomial model with ____________________ predictor variable(s).

Question 45

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.

Question 46

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} Find the coefficient of determination of this simple linear model.What does this statistic tell you about the model?

Question 47

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} Use the quadratic model to predict the value of y when x = 45.

Question 48

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} Predict the winning percentage for a hockey team with an average of 6 years of professional experience.

Question 49

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} Is there enough evidence at the 5% significance level to conclude that the model is useful in predicting the number of fatalities?

Question 50

If a quadratic relationship exists between y and each of x₁ and x₂,you use a(n)____________________-order polynomial model.

Question 51

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 a scatter diagram for the data.Does the scatter diagram suggest an estimated regression equation of the form ? Explain.

Question 52

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 .

Question 53

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} Determine the coefficient of determination quadratic model.What does this statistic tell you about this model?

Question 54

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} Determine if there is sufficient evidence at the 5% significance level to infer that the quadratic relationship between y,x,and x² in the previous question is significant.

Question 55

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} Determine if there is sufficient evidence at the 5% significance level to infer that the relationship between x and y is positive and significant.

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.

Question 57

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} Do these results allow us to conclude at the 5% significance level that the model is useful in predicting the team's winning percentage?

Question 58

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.

Question 59

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 .

Question 60

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 x² term should be retained.

Question 61

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} Interpret the coefficient b₂.

Question 62

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 x₁ term should be retained in the model.

Question 63

A first-order model was used in regression analysis involving 25 observations to study the relationship between a dependent variable y and three independent variables x₁,x₂,and x₃.The analysis showed that the mean squares for regression is 160 and the sum of squares for error is 1050.In addition,the following is a partial computer printout.
a.Develop the ANOVA table.
b.Is there enough evidence at the 5% significance level to conclude that the model is useful in predicting the value of y?
c.Test at the 5% significance level to determine whether x₁ is linearly related to y.
d.Is there sufficient evidence at the 5% significance level to indicate that x₂ is negatively linearly related to y?
e.Is there sufficient evidence at the 5% significance level to indicate that x₃ is positively linearly related to y?

Question 64

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 term should be retained in the model.

Question 65

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?

Question 66

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} What is the multiple coefficient of determination? What does this statistic tell you about the model?

Question 67

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} What does the coefficient of tell you about the model?

Question 68

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} Is there sufficient evidence at the 1% significance level to conclude that the price of a barrel of oil and the price of silver are linearly related?

Question 69

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} Is there sufficient evidence at the 1% significance level to conclude that the interaction term should be retained?

Question 70

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} Interpret the coefficient b₁.

Question 71

It is not possible to incorporate nominal variables into a regression model.

Question 72

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 interaction term should be retained in the model.

Question 73

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.

Question 74

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 term should be retained in the model.

Question 75

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} Is there sufficient evidence at the 1% significance level to conclude that the interest rate and the price of silver are linearly related?

Question 76

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.

Question 77

In regression analysis,indicator variables are also called dependent variables.

Question 78

An indicator variable (also called a dummy variable)is a variable that can assume either one of two values (usually 0 and 1),where one value represents the existence of a certain condition,and the other value indicates that the condition does not hold.

Question 79

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.

Question 80

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} What does the coefficient of tell you about the model?