Deck 20: Model Building

Question 1

For the regression equation $=20+8 x_{1}+5 x_{2}+3 x_{1} x_{2}$ , which combination of $x _ { 1 }$ and $x _ { 2 }$ , 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.

Answer 1

6 and 3.

Question 2

In explaining the amount of money spent on children's clothes each month, which of the following independent variables is best represented with an indicator variable?

A) Age.
B) Height.
C) Gender.
D) Weight.

Answer 2

C

Question 3

In explaining the income earned by university graduates, which of the following independent variables is best represented by an indicator variable in a regression model?

A) Grade point average.
B) Gender
C) Number of years since graduating from high school.
D) Age

Answer 3

B

Question 4

In explaining students' test scores, which of the following independent variables would not be adequately represented by an indicator variable?

A) Gender
B) Cultural background
C) Number of hours studying for the test
D) Marital status

Question 5

Which of the following describes the numbers that an indicator variable can have in a regression model?

A) 0 and 1
B) 1 and 2
C) 0, 1 and 2
D) None of these choices are correct.

Question 6

The following model $y = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }$ + $\varepsilon$ 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 7

For the estimated regression equation ŷ = 8 − 5x₁ + 2x₂, which of the following best describes the corresponding change in the value of y, in response to a one unit increase in x₁, while keeping x₂ constant?

A) An estimated increase in y by 5 units, on average.
B) An estimated decrease in y by 5 units, on average.
C) An estimated decrease in y by 3 units, on average.
D) An estimated decrease in y by 1 unit, on average.

Question 8

Suppose that the sample regression equation of a second-order model is $= 2.50 + 0.15 x + 0.45 x ^ { 2 }$ . 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 9

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

A) straight line going upwards.
B) straight line going downwards.
C) circle.
D) parabola.

Question 10

The model $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }$ + $\varepsilon$ 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 11

Suppose that the sample regression line of a first order model is $= 8 + 2 x _ { 1 } + 3 x _ { 2 }$ . If we examine the relationship between y and $x _ { 1 }$ for four different values of $x _ { 2 }$ , we observe that the:

A) effect of x $1$ on y remains the same no matter what the value of x $2$ .
B) effect of x $1$ on y remains the same no matter what the value of x $1$ .
C) only difference in the four equations produced is the coefficient of x $2$ .
D) None of these choices are correct.

Question 12

The model y = $\beta$ 1U1B10 + $\beta$ 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) (p -1) predictor variables.

Question 13

The model $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 }$ + $\varepsilon$ 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.

Question 14

In a first-order model with two predictors, $x _ { 1 }$ and $x _ { 2 }$ , which of the following best describes when an interaction term may be used?

A) When the relationship between the dependent variable and the independent variables is linear.
B) When the effect of $x _ { 1 }$ on the dependent variable is influenced by $x _ { 2 }$ .
C) When the effect of $x _ { 2 }$ on the dependent variable is influenced by $x _ { 1 }$ .
D) When the effect of $x _ { 1 }$ on the dependent variable is influenced by $x _ { 2 }$ or when the effect of $x _ { 2 }$ on the dependent variable is influenced by $x _ { 1 }$ .

Question 15

A manufacturing company opened a second branch plant in the same city where its first plant operates. Some of the employees had been assigned involuntarily to the new plant while some others volunteered to be transformed from the first plant to the new plant. The production manager of the new plant would like to find out whether employees who volunteered for the new plant and those who were involuntarily assigned to it differ with respect to productivity. From a random sample of 50 employees, the manager estimated the following multiple regression equation: $\hat{y}$ = -2400 + 140x₁ - 250x₂
Where y is the average number of units produced by an employee a day during the second month after joining the new plant, x₁ is the employee's aptitude test score, and x₂ is a dummy variable coded 1 for involuntary assignment and 0 for voluntary assignment.
For each additional aptitude test score, the average number of units produced by an employee who joined the new plant involuntarily:

A) increases by 250.
B) increases by 140.
C) decreases by 140.
D) decreases by 250.

Question 16

In explaining starting salaries for graduates of computer science programs, which of the following independent variables would not be adequately represented with a dummy variable?

A) Grade point average.
B) Gender.
C) Race.
D) Marital status.

Question 17

Suppose that the sample regression equation of a model is $=10+4 x_{1}+3 x_{2}-x_{1} x_{2}$ . If we examine the relationship between $x _ { 1 }$ and y for three different values of $x _ { 2 }$ , we observe that the:

A) three equations produced differ only in the intercept.
B) coefficient of $x _ { 2 }$ remains unchanged.
C) coefficient of $x _ { 1 }$ varies.
D) three equations produced differ not only in the intercept term but the coefficient of $x _ { 1 }$ , also varies.

Question 18

Suppose that the estimated regression equation for 200 business graduates is ŷ = 20 000 + 2000x + 1500I,
Where y is the starting salary, x is the grade point average and I is an indicator variable that takes the value of 1 if the student is a computer information systems major and 0 if not. A business administration major graduate with a grade point average of 4 would have an average starting salary of:

A) $20 000.
B) $26 000.
C) $29 500.
D) $28 000.

Question 19

The following model $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }$ + $\varepsilon$ is used whenever the statistician believes that, on average, y is linearly related to:

A) $x _ { 1 }$ , and the predictor variables do not interact.
B) $x _ { 2 }$ , and the predictor variables do not interact.
C) $x _ { 1 }$ and the predictor variables do not interact or to $x _ { 2 }$ , and the predictor variables do not interact.
D) $x _ { 1 }$ and the predictor variables do not interact and to $x _ { 2 }$ , and the predictor variables do not interact.

Question 20

Suppose that the sample regression equation of a second-order model is: $= 2.50 + 0.15 x + 0.45 x ^ { 2 }$ . 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) predicted value of y when x = 1.

Question 21

In general, to represent a categorical independent variable that has m possible categories, which of the following is the number of dummy variables that can be used in the regression model?

A) (m + 1) dummy variables.
B) m dummy variables.
C) (1 − m) dummy variables.
D) (m - 1) dummy variables.

Question 22

Which of the following best describes Stepwise regression?

A) Stepwise regression may involve adding one independent variable at a time.
B) Stepwise regression may involve deleting one independent variable at a time.
C) Stepwise regression may involve dividing one independent variable at a time.
D) Stepwise regression may involve adding or deleting one independent variable at a time.

Question 23

The graph of the model $=\beta_{0}+\beta_{1} x_{i}+\beta_{2} x_{i}^{2}$ is shaped like a straight line going upwards.

Question 24

The model $=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{1} x_{2}$ is referred to as a second-order model with two predictor variables with interaction.

Question 25

Which of the following best describes when to use an indicator variable in a regression?

A) To include a quantitative variable in a regression model.
B) To include a qualitative variable in a regression model.
C) To include any variable in a regression model.
D) To include a y variable in a regression model.

Question 26

In a stepwise regression procedure, if two independent variables are highly correlated, then:

A) both variables will enter the equation.
B) only one variable will enter the equation.
C) neither variable will enter the equation.
D) None of these choices are correct.

Question 27

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 qualitative variables better than analysis of variance.
C) Multiple regression handles problems with more than two independent variables better than analysis of variance.
D) All of the above are advantages of multiple regression as compared with analysis of variance.

Question 28

The model y = $\beta$ ₀ + $\beta$ ₁x + $\beta$ ₂x² + … + $\beta$ _px^p + $\varepsilon$ is referred to as a polynomial model with p predictor variables.

Question 29

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

Question 30

Stepwise regression is an iterative procedure that can only add one independent variable at a time.

Question 31

In a first-order model with two predictors, $x _ { 1 }$ and $x _ { 2 }$ , an interaction term may be used when the relationship between the dependent variable $y$ and the predictor variables is linear.

Question 32

In general, to represent a nominal independent variable that has n possible categories, we would create n dummy variables.

Question 33

Suppose that the sample regression equation of a model is $=4+1.5 x_{1}+2 x_{2}-x_{1} x_{2}$ . If we examine the relationship between $x _ { 1 }$ and y for four different values of $x _ { 2 }$ , we observe that the four equations produced differ only in the intercept term.

Question 34

In regression analysis, indicator variables may be used as independent variables.

Question 35

In a stepwise regression procedure, if two independent variables are highly correlated, then one variable usually eliminates the second variable.

Question 36

Stepwise regression is especially useful when there are many independent variables.

Question 37

Which of the following is another name for a dummy variable?

A) Independent variable
B) Dependent variable
C) Indicator variable
D) Y variable

Question 38

The model $=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}$ is used whenever the statistician believes that, on average, $y$ is linearly related to $x _ { 1 }$ and $x _ { 2 }$ , and the predictor variables do not interact.

Question 39

The model $=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}$ is referred to as a first-order model with two predictor variables with no interaction.

Question 40

Suppose that the sample regression line of a first-order model is $=4+3 x_{1}+2 x_{2}$ . If we examine the relationship between y and $x _ { 1 }$ for three different values of $x _ { 2 }$ , we observe that the effect of $x _ { 1 }$ on $y$ remains the same no matter what the value of $x _ { 2 }$ .

Question 41

In the first-order model $\hat{y}$ = 60 + 40x₁ -10x₂ + 5x₁x₂, a unit increase in x₁, while holding x₂ constant at 1, increases the value of $y$ on average by 45 units.

Question 42

A regression analysis involving 40 observations and five independent variables revealed that the total variation in the dependent variable y is 1080 and that the mean square for error is 30. Test the significance of the overall equation at the 5% level of significance.

Question 43

In explaining the amount of money spent on children's toys during Christmas each year, the independent variable 'gender' is best represented by a dummy variable.

Question 44

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

Question 45

Consider the following data for two variables, x and y, where x is the age of a particular make of car
and y is the selling price, in thousands of dollars. $$\begin{array} { | c | c c c c c c c c c c | } \hline x & 7 & 10 & 3 & 5 & 3 & 10 & 4 & 14 & 5 & 8 \\\hline y & 35.0 & 28.5 & 45.0 & 45.0 & 55.0 & 25.0 & 37.5 & 27.5 & 30.0 & 27.5 \\\hline\end{array}$$ a. Use Excel to develop an estimated regression equation of the form $\hat{y}$ = b₀ +b₁x.
b. Interpret the intercept.
c. Interpret the slope.

Question 46

In regression analysis, we can use 11 indicator variables to represent 12 months of the year.

Question 47

Consider the following data for two variables, x and y, where x is the age of a particular make of car
and y is the selling price, in thousands of dollars. Use Excel to test whether the population slope is positive, at the 1% level of significance.

Question 48

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

Question 49

Consider the following data for two variables, x and y. Use Excel to develop a scatter diagram for the data. Does the scatter diagram suggest an estimated regression equation of the form ŷ = b₀ +b₁x + b₂x²? Explain.

Question 50

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

Question 51

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

Question 52

A regression analysis was performed to study the relationship between a dependent variable and four independent variables. The following information was obtained:
r² = 0.95, SSR = 9800, n = 50.
ANOVA Test the overall validity of the model at the 5% significance level.

Question 53

In the first-order regression model $\hat{y}$ = 12 + 6x₁ +8x₂ + 4x₁x₂, a unit increase in x₁ increases the value of $y$ on average by 6 units.

Question 54

A regression analysis involving 40 observations and five independent variables revealed that the total variation in the dependent variable y is 1080 and that the mean square for error is 30.
Create the ANOVA table.

Question 55

Consider the following data for two variables, x and y. Use Excel to find the coefficient of determination. What does this statistic tell you about this simple linear model?

Question 56

Suppose that the sample regression equation of a model is $=4.7+2.2 x_{1}+2.6 x_{2}-x_{1} x_{2}$ . If we examine the relationship between y and $x _ { 2 }$ for $x _ { 1 }$ = 1, 2 and 3, we observe that the three equations produced not only differ in the intercept term, but the coefficient of $x _ { 2 }$ also varies.

Question 57

A regression analysis was performed to study the relationship between a dependent variable and four independent variables. The following information was obtained:
r² = 0.95, SSR = 9800, n = 50.
Create the ANOVA table.

Question 58

Consider the following data for two variables, x and y. $$\begin{array} { | c | c c c c c c c c c c | } \hline x & 7 & 10 & 3 & 5 & 3 & 10 & 4 & 14 & 5 & 8 \\\hline y & 35.0 & 28.5 & 45.0 & 45.0 & 55.0 & 25.0 & 37.5 & 27.5 & 30.0 & 27.5 \\\hline\end{array}$$ Use Excel to develop an estimated regression equation of the form $\hat{y}$ = b₀ +b₁x + b₂x²..

Question 59

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 60

In the first-order model $=75-12 x_{1}+5 x_{2}-3 x_{1} x_{2}$ , a unit increase in $x _ { 1 }$ , while holding $x _ { 2 }$ constant at a value of 2, decreases the value of $y$ on average by 8 units.

Question 61

An economist is analysing the incomes of professionals (physicians, dentists and lawyers). He realises 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 professionals and estimates the multiple regression model: .
where
y
= annual income (in $1000). = years of experience. = 1 if physician.
= 0 if not. = 1 if dentist.
= 0 if not.
The computer output is shown below.
THE REGRESSION EQUATION IS . S = 42.6 R-Sq = 30.9%. Is there enough evidence at the1% significant level to conclude that physicians earn more on average than lawyers?

Question 62

An economist is analysing the incomes of professionals (physicians, dentists and lawyers). He realises 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 professionals and estimates the multiple regression model: .
where
y
= annual income (in $1000). = years of experience. = 1 if physician.
= 0 if not. = 1 if dentist.
= 0 if not.
The computer output is shown below.
THE REGRESSION EQUATION IS . S = 42.6 R-Sq = 30.9%. Is there enough evidence at the 10% significance level to conclude that dentists earn less on average than lawyers?

Question 63

Consider the following data for two variables, x and y. $$\begin{array} { | c | c c c c c c c c c c | } \hline x & 7 & 10 & 3 & 5 & 3 & 10 & 4 & 14 & 5 & 8 \\\hline y & 35.0 & 28.5 & 45.0 & 45.0 & 55.0 & 25.0 & 37.5 & 27.5 & 30.0 & 27.5 \\\hline\end{array}$$ Use the model in $\hat{y}$ = 66.799 -7.307x + 0.324x² to predict the value of y when x = 10.

Question 64

A traffic consultant has analysed the factors that affect the number of traffic fatalities. She has come to the conclusion that two important variables are the number of cars and the number of tractor-trailer trucks. She proposed the second-order model with interaction: .
Where:
y = number of annual fatalities per shire. = number of cars registered in the shire (in units of 10 000). = number of trucks registered in the shire (in units of 1000).
The computer output (based on a random sample of 35 shires) is shown below.
THE REGRESSION EQUATION IS . S = 15.2 R-Sq = 47.2%.
ANALYSIS OF VARIANCE Test at the 1% significance level to determine whether the term should be retained in the model.

Question 65

An avid football fan was in the process of examining the factors that determine the success or failure of football teams. He noticed that teams with many rookies and teams with many veterans seem to do quite poorly. To further analyse his beliefs, he took a random sample of 20 teams and proposed a second-order model with one independent variable. The selected model is: .
where
y = winning team's percentage.
x = average years of professional experience.
The computer output is shown below:
THE REGRESSION EQUATION IS: S = 16.1 R-Sq = 43.9%.
ANALYSIS OF VARIANCE 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 66

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

Question 67

A traffic consultant has analysed the factors that affect the number of traffic fatalities. She has come to the conclusion that two important variables are the number of cars and the number of tractor-trailer trucks. She proposed the second-order model with interaction: .
Where:
y = number of annual fatalities per shire. = number of cars registered in the shire (in units of 10 000). = number of trucks registered in the shire (in units of 1000).
The computer output (based on a random sample of 35 shires) is shown below.
THE REGRESSION EQUATION IS . S = 15.2 R-Sq = 47.2%.
ANALYSIS OF VARIANCE What does the coefficient of tell you about the model?

Question 68

An avid football fan was in the process of examining the factors that determine the success or failure of football teams. He noticed that teams with many rookies and teams with many veterans seem to do quite poorly. To further analyse his beliefs, he took a random sample of 20 teams and proposed a second-order model with one independent variable. The selected model is: .
where
y = winning team's percentage.
x = average years of professional experience.
The computer output is shown below:
THE REGRESSION EQUATION IS: S = 16.1 R-Sq = 43.9%.
ANALYSIS OF VARIANCE Test to determine at the 10% significance level whether the term should be retained.

Question 69

A traffic consultant has analysed the factors that affect the number of traffic fatalities. She has come to the conclusion that two important variables are the number of cars and the number of tractor-trailer trucks. She proposed the second-order model with interaction: .
Where:
y = number of annual fatalities per shire. = number of cars registered in the shire (in units of 10 000). = number of trucks registered in the shire (in units of 1000).
The computer output (based on a random sample of 35 shires) is shown below.
THE REGRESSION EQUATION IS . S = 15.2 R-Sq = 47.2%.
ANALYSIS OF VARIANCE Test at the 1% significance level to determine whether the term should be retained in the model.

Question 70

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

Question 71

A traffic consultant has analysed the factors that affect the number of traffic fatalities. She has come to the conclusion that two important variables are the number of cars and the number of tractor-trailer trucks. She proposed the second-order model with interaction: .
Where:
y = number of annual fatalities per shire. = number of cars registered in the shire (in units of 10 000). = number of trucks registered in the shire (in units of 1000).
The computer output (based on a random sample of 35 shires) is shown below.
THE REGRESSION EQUATION IS . S = 15.2 R-Sq = 47.2%.
ANALYSIS OF VARIANCE Is there enough evidence at the 5% significance level to conclude that the model is useful in predicting the number of fatalities?

Question 72

Consider the following data for two variables, x and y. $$\begin{array} { | c | c c c c c c c c c c | } \hline x & 7 & 10 & 3 & 5 & 3 & 10 & 4 & 14 & 5 & 8 \\\hline y & 35.0 & 28.5 & 45.0 & 45.0 & 55.0 & 25.0 & 37.5 & 27.5 & 30.0 & 27.5 \\\hline\end{array}$$ Use Excel to determine whether there is sufficient evidence at the 1% significance level to infer that the relationship between y, x and $x ^ { 2 }$ in $\hat{y}$ = 66.799-7.307x + 0.324x² is significant.

Question 73

Consider the following data for two variables, x and y. Use Excel to find the coefficient of determination. What does this statistic tell you about this curvilinear model?

Question 74

A traffic consultant has analysed the factors that affect the number of traffic fatalities. She has come to the conclusion that two important variables are the number of cars and the number of tractor-trailer trucks. She proposed the second-order model with interaction: .
Where:
y = number of annual fatalities per shire. = number of cars registered in the shire (in units of 10 000). = number of trucks registered in the shire (in units of 1000).
The computer output (based on a random sample of 35 shires) is shown below.
THE REGRESSION EQUATION IS . S = 15.2 R-Sq = 47.2%.
ANALYSIS OF VARIANCE Test at the 1% significance level to determine whether the interaction term should be retained in the model.

Question 75

A traffic consultant has analysed the factors that affect the number of traffic fatalities. She has come to the conclusion that two important variables are the number of cars and the number of tractor-trailer trucks. She proposed the second-order model with interaction: .
Where:
y = number of annual fatalities per shire. = number of cars registered in the shire (in units of 10 000). = number of trucks registered in the shire (in units of 1000).
The computer output (based on a random sample of 35 shires) is shown below.
THE REGRESSION EQUATION IS . S = 15.2 R-Sq = 47.2%.
ANALYSIS OF VARIANCE Test at the 1% significance level to determine whether the term should be retained in the model.

Question 76

A traffic consultant has analysed the factors that affect the number of traffic fatalities. She has come to the conclusion that two important variables are the number of cars and the number of tractor-trailer trucks. She proposed the second-order model with interaction: .
Where:
y = number of annual fatalities per shire. = number of cars registered in the shire (in units of 10 000). = number of trucks registered in the shire (in units of 1000).
The computer output (based on a random sample of 35 shires) is shown below.
THE REGRESSION EQUATION IS . S = 15.2 R-Sq = 47.2%.
ANALYSIS OF VARIANCE What does the coefficient of tell you about the model?

Question 77

An economist is analysing the incomes of professionals (physicians, dentists and lawyers). He realises 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 professionals and estimates the multiple regression model: .
where
y
= annual income (in $1000). = years of experience. = 1 if physician.
= 0 if not. = 1 if dentist.
= 0 if not.
The computer output is shown below.
THE REGRESSION EQUATION IS . S = 42.6 R-Sq = 30.9%. Is there enough evidence at the 5% significance level to conclude that income and experience are linearly related?

Question 78

A traffic consultant has analysed the factors that affect the number of traffic fatalities. She has come to the conclusion that two important variables are the number of cars and the number of tractor-trailer trucks. She proposed the second-order model with interaction: .
Where:
y = number of annual fatalities per shire. = number of cars registered in the shire (in units of 10 000). = number of trucks registered in the shire (in units of 1000).
The computer output (based on a random sample of 35 shires) is shown below.
THE REGRESSION EQUATION IS . S = 15.2 R-Sq = 47.2%.
ANALYSIS OF VARIANCE Test at the 1% significance level to determine whether the term should be retained in the model.

Question 79

An economist is analysing the incomes of professionals (physicians, dentists and lawyers). He realises 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 professionals and estimates the multiple regression model: .
where
y
= annual income (in $1000). = years of experience. = 1 if physician.
= 0 if not. = 1 if dentist.
= 0 if not.
The computer output is shown below.
THE REGRESSION EQUATION IS . S = 42.6 R-Sq = 30.9%. Do these results allow us to conclude at the 1% significance level that the model is useful in predicting the income of professionals?

Question 80

A traffic consultant has analysed the factors that affect the number of traffic fatalities. She has come to the conclusion that two important variables are the number of cars and the number of tractor-trailer trucks. She proposed the second-order model with interaction: .
Where:
y = number of annual fatalities per shire. = number of cars registered in the shire (in units of 10 000). = number of trucks registered in the shire (in units of 1000).
The computer output (based on a random sample of 35 shires) is shown below.
THE REGRESSION EQUATION IS . S = 15.2 R-Sq = 47.2%.
ANALYSIS OF VARIANCE What is the multiple coefficient of determination? What does this statistic tell you about the model?