Deck 18: Model Building

Question 1

The model y = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\beta$ ₃x₁x₂ + $\varepsilon$ 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.

Answer 1

first-order model with two predictor variables with interaction.

Question 2

In the first-order model $\hat { y } = 8 + 3 x _ { 1 } + 5 x _ { 2 }$ ,a unit increase in x₂,while holding x₁ constant,increases the value of y on average by 5 units.

Answer 2

True

Question 3

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

Answer 3

False

Question 4

In the first-order model $\tilde { y } = 50 + 25 x _ { 1 } - 10 x _ { 2 } - 6 x _ { 1 } x _ { 2 }$ ,a unit increase in x₂,while holding x₁ constant at a value of 3,decreases the value of y on average by 3 units.

Question 5

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

Question 6

The model y = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\beta$ ₃x₁x₂ + $\varepsilon$ is referred to as a second-order model with two predictor variables with interaction.

Question 7

The model $\tilde { y } = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }$ 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

The model y = $\beta$ ₀ + $\beta$ ₁x + $\beta$ ₂x² + $\varepsilon$ is referred to as a simple linear regression model.

Question 9

In the first-order regression model $\tilde { y } = 12 + 6 x _ { 1 } + 8 x _ { 2 } + 4 x _ { 1 } x _ { 2 }$ ,a unit increase in x₁ increases the value of y on average by 6 units.

Question 10

Suppose that the sample regression equation of a model is $\tilde { y } = 4 + 1.5 x _ { 1 } + 2 x _ { 2 } - x _ { 1 } x _ { 2 }$ .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

Suppose that the sample regression equation of a model is $\tilde { y } = 4.7 + 2.2 x _ { 1 } + 2.6 x _ { 2 } - x _ { 1 } x _ { 2 }$ .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.

Question 12

The model y = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\varepsilon$ is referred to as a first-order model with two predictor variables with no interaction.

Question 13

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 14

Suppose that the sample regression line of the first-order model is $\hat { y } = 4 + 3 x _ { 1 } + 2 x _ { 2 }$ .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 15

In the first-order model $\tilde { y } = 75 - 12 x _ { 1 } + 5 x _ { 2 } - 3 x _ { 1 } x _ { 2 }$ ,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 16

The model $\gamma _ { i } = \beta _ { 0 } + \beta _ { 1 } x _ { i } + \beta _ { 2 } x _ { i } ^ { 2 } + \ldots \ldots \ldots + \beta _ { y } x _ { i } ^ { y } + \varepsilon _ { i }$ is referred to as a polynomial model with one predictor variable.

Question 17

In the first-order model $\tilde { y } = 60 + 40 x _ { 1 } - 10 x _ { 2 } + 5 x _ { 1 } x _ { 2 }$ ,a unit increase in x₂,while holding x₁ constant at 1,changes the value of y on average by -5 units.

Question 18

The graph of the model $\tilde { y } _ { i } = \beta _ { 0 } + \beta _ { 1 } x _ { i } + \beta _ { 2 } x _ { i } ^ { 2 }$ is shaped like a straight line going upwards.

Question 19

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

Question 20

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 21

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

Question 22

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

Question 23

When we plot x versus y,the graph of the model y = $\beta$ ₀ + $\beta$ ₁x + $\beta$ ₂x² + $\varepsilon$ is shaped like a:

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

Question 24

Suppose that the sample regression equation of a second-order model is given by $\tilde { y } = 2.50 + 0.15 x + 0.45 x ^ { 2 }$ .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 25

Suppose that the sample regression equation of a model is $\tilde { y } = 10 + 4 x _ { 1 } + 3 x _ { 2 } - x _ { 1 } x _ { 2 }$ .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 26

The model y = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\varepsilon$ 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 27

For the following regression equation $\tilde { y } = 75 + 20 x _ { 1 } - 15 x _ { 2 } + 5 x _ { 1 } x _ { 2 }$ ,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 28

The model y = $\beta$ ₀ + $\beta$ ₁x + $\beta$ ₂x² + $\varepsilon$ 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 29

The model y = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\beta$ ₃x₁x₂ + $\varepsilon$ is a(n)____________________-order polynomial model with ____________________ predictor variables and ____________________.

Question 30

The model y = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\varepsilon$ is a(n)____________________-order polynomial model with ____________________ predictor variable(s).

Question 31

For the following regression equation $\tilde { y } = 20 + 8 x _ { 1 } + 5 x _ { 2 } + 3 x _ { 1 } x _ { 2 }$ ,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 32

For the following regression equation $\tilde { y } = 15 + 6 x _ { 1 } + 5 x _ { 2 } + 4 x _ { 1 } x _ { 2 }$ ,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 33

Suppose that the sample regression line of the first-order model is $\hat { y } = 8 + 2 x _ { 1 } + 3 x _ { 2 }$ .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 34

For the following regression equation $\tilde { y } = 50 + 10 x _ { 1 } - 4 x _ { 2 } - 6 x _ { 1 } x _ { 2 }$ ,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 35

Which of the following statements is false regarding the graph of the second-order polynomial model y = $\beta$ ₀ + $\beta$ ₁x + $\beta$ ₂x² + $\varepsilon$ ?

A) If $\beta$ ₂ is negative,the graph is concave,while if $\beta$ ₂ is positive,the graph is convex.
B) The greater the absolute value of $\beta$ ₂,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 36

For the following regression equation $\tilde { y } = 100 - 12 x _ { 1 } + 5 x _ { 2 } - 4 x _ { 1 } x _ { 2 }$ ,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 37

For the following regression equation $\tilde { y } = 10 + 3 x _ { 1 } + 4 x _ { 2 }$ ,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 38

The model y = $\beta$ ₀ + $\beta$ ₁x + $\beta$ ₂x² +.........+ $\beta$ _px^p + $\varepsilon$ 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 39

Suppose that the sample regression equation of a second-order model is given by $\tilde { y } = 2.50 + 0.15 x + 0.45 x ^ { 2 }$ .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 40

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

Question 41

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 42

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 $$\tilde { y } = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } ^ { 2 } + \beta _ { 4 } x _ { 2 } ^ { 2 } + \beta _ { 5 } x _ { 1 } x _ { 2 } + \varepsilon$$ (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 $$y = 69.7 + 11.3 x _ { 1 } + 7.61 x _ { 2 } - 1.15 x _ { 1 } ^ { 2 } - 0.51 x _ { 2 } ^ { 2 } - 0.13 x _ { 1 } x _ { 2 }$$ $\begin{array}{ccc}\text { Predictor}&\text { Coef } & \text { StDev } & T \\\hline\text { Constant}& 69.7 & 41.3 & 1.688 \\x_{1} &11.3 & 5.1 & 2.216 \\ x_{2}&7.61 & 2.55 & 2.984 \\x_1^2&-1.15 & .64 & -1.797 \\& & \\x_2^2&-.51 & .20 & -2.55 \\& & \\& & \\ x_{1} x_{2}&-.13 & .10 & -1.30\end{array}$ $$S= 15.2 \quad \mathrm { R } - \mathrm { Sq } = 47.2 \%$$ ANALYSIS OF VARIANCE
$$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \boldsymbol { df } & \mathbf { S S } & \boldsymbol { M S } & \boldsymbol { F } \\\hline \text { Repressian } & 5 & 5959 & 1191.800 & 5.181 \\\text { Error } & 29 & 6671 & 230.034 & \\\hline \text { Total } & 34 & 12630 & & \\\hline\end{array}$$

-{Motorcycle Fatalities Narrative} Test at the 1% significance level to determine if the x₂ term should be retained in the model.

Question 43

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 $$\tilde { y } = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } ^ { 2 } + \beta _ { 4 } x _ { 2 } ^ { 2 } + \beta _ { 5 } x _ { 1 } x _ { 2 } + \varepsilon$$ (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 $$y = 69.7 + 11.3 x _ { 1 } + 7.61 x _ { 2 } - 1.15 x _ { 1 } ^ { 2 } - 0.51 x _ { 2 } ^ { 2 } - 0.13 x _ { 1 } x _ { 2 }$$ $\begin{array}{ccc}\text { Predictor}&\text { Coef } & \text { StDev } & T \\\hline\text { Constant}& 69.7 & 41.3 & 1.688 \\x_{1} &11.3 & 5.1 & 2.216 \\ x_{2}&7.61 & 2.55 & 2.984 \\x_1^2&-1.15 & .64 & -1.797 \\& & \\x_2^2&-.51 & .20 & -2.55 \\& & \\& & \\ x_{1} x_{2}&-.13 & .10 & -1.30\end{array}$ $$S= 15.2 \quad \mathrm { R } - \mathrm { Sq } = 47.2 \%$$ ANALYSIS OF VARIANCE
$$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \boldsymbol { df } & \mathbf { S S } & \boldsymbol { M S } & \boldsymbol { F } \\\hline \text { Repressian } & 5 & 5959 & 1191.800 & 5.181 \\\text { Error } & 29 & 6671 & 230.034 & \\\hline \text { Total } & 34 & 12630 & & \\\hline\end{array}$$

-{Motorcycle Fatalities Narrative} Test at the 1% significance level to determine if the x₁ term should be retained in the model.

Question 44

{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 45

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

Question 46

{Computer Training Narrative} Develop a scatter diagram for the data.Does the scatter diagram suggest an estimated regression equation of the form ? Explain.

Question 47

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 = $\beta$ ₀ + $\beta$ ₁x + $\beta$ ₂x² + $\varepsilon$ ,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
$$\begin{array} { | c | c c c | } \hline \text { Predictar } & \text { Coef } & \text { StDev } & \boldsymbol { T } \\\hline \text { Constant } & 32.6 & 19.3 & 1.689 \\\boldsymbol { x} & 5.96 & 2.41 & 2.473 \\\boldsymbol { \boldsymbol { x} ^ { 2 } } & - .48 & .22 & - 2.182 \\\hline\end{array}$$ S = 16.1 $\quad$ R - S q = 43.9 % ANALYSIS OF VARIANCE
$$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \boldsymbol { df } & \mathbf { S S } & \boldsymbol { M S } & \boldsymbol { F } \\\hline \text { Regressian } & 2 & 3452 & 1726 & 6.663 \\\text { Error } & 17 & 4404 & 259.059 & \\\hline \text { Total } & 19 & 7856 & & \\\hline\end{array}$$

-{Hockey Teams Narrative} Test to determine at the 10% significance level if the x² term should be retained.

Question 48

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

Question 49

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 = $\beta$ ₀ + $\beta$ ₁x + $\beta$ ₂x² + $\varepsilon$ ,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
$$\begin{array} { | c | c c c | } \hline \text { Predictar } & \text { Coef } & \text { StDev } & \boldsymbol { T } \\\hline \text { Constant } & 32.6 & 19.3 & 1.689 \\\boldsymbol { x} & 5.96 & 2.41 & 2.473 \\\boldsymbol { \boldsymbol { x} ^ { 2 } } & - .48 & .22 & - 2.182 \\\hline\end{array}$$ S = 16.1 $\quad$ R - S q = 43.9 % ANALYSIS OF VARIANCE
$$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \boldsymbol { df } & \mathbf { S S } & \boldsymbol { M S } & \boldsymbol { F } \\\hline \text { Regressian } & 2 & 3452 & 1726 & 6.663 \\\text { Error } & 17 & 4404 & 259.059 & \\\hline \text { Total } & 19 & 7856 & & \\\hline\end{array}$$

-{Hockey Teams Narrative} Predict the winning percentage for a hockey team with an average of 6 years of professional experience.

Question 50

{Computer Training Narrative} Use the quadratic model to predict the value of y when x = 45.

Question 51

{Computer Training Narrative} Develop an estimated regression equation of the form .

Question 52

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

Question 53

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 54

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 = $\beta$ ₀ + $\beta$ ₁x + $\beta$ ₂x² + $\varepsilon$ ,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
$$\begin{array} { | c | c c c | } \hline \text { Predictar } & \text { Coef } & \text { StDev } & \boldsymbol { T } \\\hline \text { Constant } & 32.6 & 19.3 & 1.689 \\\boldsymbol { x} & 5.96 & 2.41 & 2.473 \\\boldsymbol { \boldsymbol { x} ^ { 2 } } & - .48 & .22 & - 2.182 \\\hline\end{array}$$ S = 16.1 $\quad$ R - S q = 43.9 % ANALYSIS OF VARIANCE
$$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \boldsymbol { df } & \mathbf { S S } & \boldsymbol { M S } & \boldsymbol { F } \\\hline \text { Regressian } & 2 & 3452 & 1726 & 6.663 \\\text { Error } & 17 & 4404 & 259.059 & \\\hline \text { Total } & 19 & 7856 & & \\\hline\end{array}$$

-{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 55

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 = $\beta$ ₀ + $\beta$ ₁x + $\beta$ ₂x² + $\varepsilon$ ,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
$$\begin{array} { | c | c c c | } \hline \text { Predictar } & \text { Coef } & \text { StDev } & \boldsymbol { T } \\\hline \text { Constant } & 32.6 & 19.3 & 1.689 \\\boldsymbol { x} & 5.96 & 2.41 & 2.473 \\\boldsymbol { \boldsymbol { x} ^ { 2 } } & - .48 & .22 & - 2.182 \\\hline\end{array}$$ S = 16.1 $\quad$ R - S q = 43.9 % ANALYSIS OF VARIANCE
$$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \boldsymbol { df } & \mathbf { S S } & \boldsymbol { M S } & \boldsymbol { F } \\\hline \text { Regressian } & 2 & 3452 & 1726 & 6.663 \\\text { Error } & 17 & 4404 & 259.059 & \\\hline \text { Total } & 19 & 7856 & & \\\hline\end{array}$$

-{Hockey Teams Narrative} Test to determine at the 10% significance level if the linear term should be retained.

Question 56

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

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 = $\beta$ ₀ + $\beta$ ₁x + $\beta$ ₂x² + $\varepsilon$ ,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
$$\begin{array} { | c | c c c | } \hline \text { Predictar } & \text { Coef } & \text { StDev } & \boldsymbol { T } \\\hline \text { Constant } & 32.6 & 19.3 & 1.689 \\\boldsymbol { x} & 5.96 & 2.41 & 2.473 \\\boldsymbol { \boldsymbol { x} ^ { 2 } } & - .48 & .22 & - 2.182 \\\hline\end{array}$$ S = 16.1 $\quad$ R - S q = 43.9 % ANALYSIS OF VARIANCE
$$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \boldsymbol { df } & \mathbf { S S } & \boldsymbol { M S } & \boldsymbol { F } \\\hline \text { Regressian } & 2 & 3452 & 1726 & 6.663 \\\text { Error } & 17 & 4404 & 259.059 & \\\hline \text { Total } & 19 & 7856 & & \\\hline\end{array}$$

-{Hockey Teams Narrative} What is the coefficient of determination? Explain what this statistic tells you about the model.

Question 58

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

Question 59

{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 60

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 $$\tilde { y } = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } ^ { 2 } + \beta _ { 4 } x _ { 2 } ^ { 2 } + \beta _ { 5 } x _ { 1 } x _ { 2 } + \varepsilon$$ (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 $$y = 69.7 + 11.3 x _ { 1 } + 7.61 x _ { 2 } - 1.15 x _ { 1 } ^ { 2 } - 0.51 x _ { 2 } ^ { 2 } - 0.13 x _ { 1 } x _ { 2 }$$ $\begin{array}{ccc}\text { Predictor}&\text { Coef } & \text { StDev } & T \\\hline\text { Constant}& 69.7 & 41.3 & 1.688 \\x_{1} &11.3 & 5.1 & 2.216 \\ x_{2}&7.61 & 2.55 & 2.984 \\x_1^2&-1.15 & .64 & -1.797 \\& & \\x_2^2&-.51 & .20 & -2.55 \\& & \\& & \\ x_{1} x_{2}&-.13 & .10 & -1.30\end{array}$ $$S= 15.2 \quad \mathrm { R } - \mathrm { Sq } = 47.2 \%$$ ANALYSIS OF VARIANCE
$$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \boldsymbol { df } & \mathbf { S S } & \boldsymbol { M S } & \boldsymbol { F } \\\hline \text { Repressian } & 5 & 5959 & 1191.800 & 5.181 \\\text { Error } & 29 & 6671 & 230.034 & \\\hline \text { Total } & 34 & 12630 & & \\\hline\end{array}$$

-{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 61

In order to represent a nominal variable with m categories,we must create m - 1 indicator variables.

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 $$\tilde { y } = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } ^ { 2 } + \beta _ { 4 } x _ { 2 } ^ { 2 } + \beta _ { 5 } x _ { 1 } x _ { 2 } + \varepsilon$$ (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 $$y = 69.7 + 11.3 x _ { 1 } + 7.61 x _ { 2 } - 1.15 x _ { 1 } ^ { 2 } - 0.51 x _ { 2 } ^ { 2 } - 0.13 x _ { 1 } x _ { 2 }$$ $\begin{array}{ccc}\text { Predictor}&\text { Coef } & \text { StDev } & T \\\hline\text { Constant}& 69.7 & 41.3 & 1.688 \\x_{1} &11.3 & 5.1 & 2.216 \\ x_{2}&7.61 & 2.55 & 2.984 \\x_1^2&-1.15 & .64 & -1.797 \\& & \\x_2^2&-.51 & .20 & -2.55 \\& & \\& & \\ x_{1} x_{2}&-.13 & .10 & -1.30\end{array}$ $$S= 15.2 \quad \mathrm { R } - \mathrm { Sq } = 47.2 \%$$ ANALYSIS OF VARIANCE
$$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \boldsymbol { df } & \mathbf { S S } & \boldsymbol { M S } & \boldsymbol { F } \\\hline \text { Repressian } & 5 & 5959 & 1191.800 & 5.181 \\\text { Error } & 29 & 6671 & 230.034 & \\\hline \text { Total } & 34 & 12630 & & \\\hline\end{array}$$

-{Motorcycle Fatalities Narrative} What does the coefficient of $x _ { 1 } ^ { 2 }$ tell you about the model?

Question 63

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 = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\beta$ ₃x₁x₃ + $\varepsilon$ .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
$$\begin{array} { | c | c c c | } \hline \text { Predictar } & \text { Coef } & \text { StDev } & T \\\hline \text { Constant } & 115.6 & 78.1 & 1.480 \\\boldsymbol { x } _ { 1 } & 22.3 & 7.1 & 3.141 \\\boldsymbol { x } _ { 2 } & 14.7 & 6.3 & 2.333 \\\boldsymbol { x } _ { 1 } x _ { 2 } & - 1.36 & .52 & - 2.615 \\\hline\end{array}$$ $$S= 20.9 \quad R - S q = 55.4 \%$$ ANALYSIS OF VARIANCE
$$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \boldsymbol { df } & \mathbf { S S } & \boldsymbol { M S } & \boldsymbol { F } \\\hline \text { Regressian } & 3 & 8661 & 2887.0 & 6.626 \\\text { Errorr } & 16 & 6971 & 435.7 & \\\hline \text { Total } & 19 & 15632 & & \\\hline\end{array}$$

-{Silver Prices Narrative} Interpret the coefficient b₂.

Question 64

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 65

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 $$\tilde { y } = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } ^ { 2 } + \beta _ { 4 } x _ { 2 } ^ { 2 } + \beta _ { 5 } x _ { 1 } x _ { 2 } + \varepsilon$$ (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 $$y = 69.7 + 11.3 x _ { 1 } + 7.61 x _ { 2 } - 1.15 x _ { 1 } ^ { 2 } - 0.51 x _ { 2 } ^ { 2 } - 0.13 x _ { 1 } x _ { 2 }$$ $\begin{array}{ccc}\text { Predictor}&\text { Coef } & \text { StDev } & T \\\hline\text { Constant}& 69.7 & 41.3 & 1.688 \\x_{1} &11.3 & 5.1 & 2.216 \\ x_{2}&7.61 & 2.55 & 2.984 \\x_1^2&-1.15 & .64 & -1.797 \\& & \\x_2^2&-.51 & .20 & -2.55 \\& & \\& & \\ x_{1} x_{2}&-.13 & .10 & -1.30\end{array}$ $$S= 15.2 \quad \mathrm { R } - \mathrm { Sq } = 47.2 \%$$ ANALYSIS OF VARIANCE
$$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \boldsymbol { df } & \mathbf { S S } & \boldsymbol { M S } & \boldsymbol { F } \\\hline \text { Repressian } & 5 & 5959 & 1191.800 & 5.181 \\\text { Error } & 29 & 6671 & 230.034 & \\\hline \text { Total } & 34 & 12630 & & \\\hline\end{array}$$

-{Motorcycle Fatalities Narrative} Test at the 1% significance level to determine if the interaction term should be retained in the model.

Question 66

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 67

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 = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\beta$ ₃x₁x₃ + $\varepsilon$ .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
$$\begin{array} { | c | c c c | } \hline \text { Predictar } & \text { Coef } & \text { StDev } & T \\\hline \text { Constant } & 115.6 & 78.1 & 1.480 \\\boldsymbol { x } _ { 1 } & 22.3 & 7.1 & 3.141 \\\boldsymbol { x } _ { 2 } & 14.7 & 6.3 & 2.333 \\\boldsymbol { x } _ { 1 } x _ { 2 } & - 1.36 & .52 & - 2.615 \\\hline\end{array}$$ $$S= 20.9 \quad R - S q = 55.4 \%$$ ANALYSIS OF VARIANCE
$$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \boldsymbol { df } & \mathbf { S S } & \boldsymbol { M S } & \boldsymbol { F } \\\hline \text { Regressian } & 3 & 8661 & 2887.0 & 6.626 \\\text { Errorr } & 16 & 6971 & 435.7 & \\\hline \text { Total } & 19 & 15632 & & \\\hline\end{array}$$

-{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 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 = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\beta$ ₃x₁x₃ + $\varepsilon$ .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
$$\begin{array} { | c | c c c | } \hline \text { Predictar } & \text { Coef } & \text { StDev } & T \\\hline \text { Constant } & 115.6 & 78.1 & 1.480 \\\boldsymbol { x } _ { 1 } & 22.3 & 7.1 & 3.141 \\\boldsymbol { x } _ { 2 } & 14.7 & 6.3 & 2.333 \\\boldsymbol { x } _ { 1 } x _ { 2 } & - 1.36 & .52 & - 2.615 \\\hline\end{array}$$ $$S= 20.9 \quad R - S q = 55.4 \%$$ ANALYSIS OF VARIANCE
$$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \boldsymbol { df } & \mathbf { S S } & \boldsymbol { M S } & \boldsymbol { F } \\\hline \text { Regressian } & 3 & 8661 & 2887.0 & 6.626 \\\text { Errorr } & 16 & 6971 & 435.7 & \\\hline \text { Total } & 19 & 15632 & & \\\hline\end{array}$$

-{Silver Prices Narrative} Interpret the coefficient b₁.

Question 69

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 70

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 $$\tilde { y } = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } ^ { 2 } + \beta _ { 4 } x _ { 2 } ^ { 2 } + \beta _ { 5 } x _ { 1 } x _ { 2 } + \varepsilon$$ (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 $$y = 69.7 + 11.3 x _ { 1 } + 7.61 x _ { 2 } - 1.15 x _ { 1 } ^ { 2 } - 0.51 x _ { 2 } ^ { 2 } - 0.13 x _ { 1 } x _ { 2 }$$ $\begin{array}{ccc}\text { Predictor}&\text { Coef } & \text { StDev } & T \\\hline\text { Constant}& 69.7 & 41.3 & 1.688 \\x_{1} &11.3 & 5.1 & 2.216 \\ x_{2}&7.61 & 2.55 & 2.984 \\x_1^2&-1.15 & .64 & -1.797 \\& & \\x_2^2&-.51 & .20 & -2.55 \\& & \\& & \\ x_{1} x_{2}&-.13 & .10 & -1.30\end{array}$ $$S= 15.2 \quad \mathrm { R } - \mathrm { Sq } = 47.2 \%$$ ANALYSIS OF VARIANCE
$$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \boldsymbol { df } & \mathbf { S S } & \boldsymbol { M S } & \boldsymbol { F } \\\hline \text { Repressian } & 5 & 5959 & 1191.800 & 5.181 \\\text { Error } & 29 & 6671 & 230.034 & \\\hline \text { Total } & 34 & 12630 & & \\\hline\end{array}$$

-{Motorcycle Fatalities Narrative} Test at the 1% significance level to determine if the $x _ { 2 } ^ { 2 }$ term should be retained in the model.

Question 71

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 = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\beta$ ₃x₁x₃ + $\varepsilon$ .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
$$\begin{array} { | c | c c c | } \hline \text { Predictar } & \text { Coef } & \text { StDev } & T \\\hline \text { Constant } & 115.6 & 78.1 & 1.480 \\\boldsymbol { x } _ { 1 } & 22.3 & 7.1 & 3.141 \\\boldsymbol { x } _ { 2 } & 14.7 & 6.3 & 2.333 \\\boldsymbol { x } _ { 1 } x _ { 2 } & - 1.36 & .52 & - 2.615 \\\hline\end{array}$$ $$S= 20.9 \quad R - S q = 55.4 \%$$ ANALYSIS OF VARIANCE
$$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \boldsymbol { df } & \mathbf { S S } & \boldsymbol { M S } & \boldsymbol { F } \\\hline \text { Regressian } & 3 & 8661 & 2887.0 & 6.626 \\\text { Errorr } & 16 & 6971 & 435.7 & \\\hline \text { Total } & 19 & 15632 & & \\\hline\end{array}$$

-{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 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 $$\tilde { y } = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } ^ { 2 } + \beta _ { 4 } x _ { 2 } ^ { 2 } + \beta _ { 5 } x _ { 1 } x _ { 2 } + \varepsilon$$ (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 $$y = 69.7 + 11.3 x _ { 1 } + 7.61 x _ { 2 } - 1.15 x _ { 1 } ^ { 2 } - 0.51 x _ { 2 } ^ { 2 } - 0.13 x _ { 1 } x _ { 2 }$$ $\begin{array}{ccc}\text { Predictor}&\text { Coef } & \text { StDev } & T \\\hline\text { Constant}& 69.7 & 41.3 & 1.688 \\x_{1} &11.3 & 5.1 & 2.216 \\ x_{2}&7.61 & 2.55 & 2.984 \\x_1^2&-1.15 & .64 & -1.797 \\& & \\x_2^2&-.51 & .20 & -2.55 \\& & \\& & \\ x_{1} x_{2}&-.13 & .10 & -1.30\end{array}$ $$S= 15.2 \quad \mathrm { R } - \mathrm { Sq } = 47.2 \%$$ ANALYSIS OF VARIANCE
$$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \boldsymbol { df } & \mathbf { S S } & \boldsymbol { M S } & \boldsymbol { F } \\\hline \text { Repressian } & 5 & 5959 & 1191.800 & 5.181 \\\text { Error } & 29 & 6671 & 230.034 & \\\hline \text { Total } & 34 & 12630 & & \\\hline\end{array}$$

-{Motorcycle Fatalities Narrative} What does the coefficient of $x _ { 2 } ^ { 2 }$ tell you about the model?

Question 73

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

Question 74

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 = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\beta$ ₃x₁x₃ + $\varepsilon$ .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
$$\begin{array} { | c | c c c | } \hline \text { Predictar } & \text { Coef } & \text { StDev } & T \\\hline \text { Constant } & 115.6 & 78.1 & 1.480 \\\boldsymbol { x } _ { 1 } & 22.3 & 7.1 & 3.141 \\\boldsymbol { x } _ { 2 } & 14.7 & 6.3 & 2.333 \\\boldsymbol { x } _ { 1 } x _ { 2 } & - 1.36 & .52 & - 2.615 \\\hline\end{array}$$ $$S= 20.9 \quad R - S q = 55.4 \%$$ ANALYSIS OF VARIANCE
$$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \boldsymbol { df } & \mathbf { S S } & \boldsymbol { M S } & \boldsymbol { F } \\\hline \text { Regressian } & 3 & 8661 & 2887.0 & 6.626 \\\text { Errorr } & 16 & 6971 & 435.7 & \\\hline \text { Total } & 19 & 15632 & & \\\hline\end{array}$$

-{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 75

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

Question 76

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 = $\beta$ ₀ + $\beta$ ₁x₁ + $\beta$ ₂x₂ + $\beta$ ₃x₁x₃ + $\varepsilon$ .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
$$\begin{array} { | c | c c c | } \hline \text { Predictar } & \text { Coef } & \text { StDev } & T \\\hline \text { Constant } & 115.6 & 78.1 & 1.480 \\\boldsymbol { x } _ { 1 } & 22.3 & 7.1 & 3.141 \\\boldsymbol { x } _ { 2 } & 14.7 & 6.3 & 2.333 \\\boldsymbol { x } _ { 1 } x _ { 2 } & - 1.36 & .52 & - 2.615 \\\hline\end{array}$$ $$S= 20.9 \quad R - S q = 55.4 \%$$ ANALYSIS OF VARIANCE
$$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \boldsymbol { df } & \mathbf { S S } & \boldsymbol { M S } & \boldsymbol { F } \\\hline \text { Regressian } & 3 & 8661 & 2887.0 & 6.626 \\\text { Errorr } & 16 & 6971 & 435.7 & \\\hline \text { Total } & 19 & 15632 & & \\\hline\end{array}$$

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

Question 77

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 $$\tilde { y } = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } ^ { 2 } + \beta _ { 4 } x _ { 2 } ^ { 2 } + \beta _ { 5 } x _ { 1 } x _ { 2 } + \varepsilon$$ (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 $$y = 69.7 + 11.3 x _ { 1 } + 7.61 x _ { 2 } - 1.15 x _ { 1 } ^ { 2 } - 0.51 x _ { 2 } ^ { 2 } - 0.13 x _ { 1 } x _ { 2 }$$ $\begin{array}{ccc}\text { Predictor}&\text { Coef } & \text { StDev } & T \\\hline\text { Constant}& 69.7 & 41.3 & 1.688 \\x_{1} &11.3 & 5.1 & 2.216 \\ x_{2}&7.61 & 2.55 & 2.984 \\x_1^2&-1.15 & .64 & -1.797 \\& & \\x_2^2&-.51 & .20 & -2.55 \\& & \\& & \\ x_{1} x_{2}&-.13 & .10 & -1.30\end{array}$ $$S= 15.2 \quad \mathrm { R } - \mathrm { Sq } = 47.2 \%$$ ANALYSIS OF VARIANCE
$$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & \boldsymbol { df } & \mathbf { S S } & \boldsymbol { M S } & \boldsymbol { F } \\\hline \text { Repressian } & 5 & 5959 & 1191.800 & 5.181 \\\text { Error } & 29 & 6671 & 230.034 & \\\hline \text { Total } & 34 & 12630 & & \\\hline\end{array}$$

-{Motorcycle Fatalities Narrative} Test at the 1% significance level to determine if the $x _ { 1 } ^ { 2 }$ term should be retained in the model.

Question 78

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 ANALYSIS OF VARIANCE

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

Question 79

In general,to represent a nominal independent variable that has c possible categories,we would create (c -1)dummy variables.

Question 80

When a dummy variable is included in a multiple regression model,the interpretation of the estimated slope coefficient does not make any sense anymore.