Deck 20: Model Building

Question 1

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 1

B

Question 2

The model + 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 2

B

Question 3

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.

Answer 3

D

Question 4

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 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 model + 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 7

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

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

Question 8

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 9

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 10

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 11

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 12

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 13

When we plot x versus y, the graph of the model + is shaped like a:

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

Question 14

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.

Question 15

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 16

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 17

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.

Question 18

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 19

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 20

The following model + is used whenever the statistician believes that, on average, y is linearly related to:

A) , and the predictor variables do not interact.
B) , and the predictor variables do not interact.
C) and the predictor variables do not interact or to , and the predictor variables do not interact.
D) and the predictor variables do not interact and to , and the predictor variables do not interact.

Question 21

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

Question 22

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 23

In the first-order model ŷ = 8 + 3x₁ +5x₂, a unit increase in , while holding constant, increases the value of on average by 3 units.

Question 24

In the first-order model = 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 25

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

Question 26

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

Question 27

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 28

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

Question 29

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 30

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

Question 31

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

Question 32

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 33

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

Question 34

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 35

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 36

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

Question 37

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 38

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

Question 39

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

Question 40

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 41

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 ? = b₀ +b₁x + b₂x²..

Question 42

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 43

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 = 66.799 -7.307x + 0.324x² to predict the value of y when x = 10.

Question 44

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 45

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 = 66.799 -7.307x + 0.324x² is significant.

Question 46

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

Question 47

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 48

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 49

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 50

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 51

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 52

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 53

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 54

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 55

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 56

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

Question 57

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: $y = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 } + \varepsilon$ .
where
y = winning team's percentage.
x = average years of professional experience.
The computer output is shown below:
THE REGRESSION EQUATION IS: $y =$ $32.6 + 5.96 x - 0.48 x ^ { 2 }$ $$\begin{array} { | c | r c r | } \hline \text { Predictor } & \text { Coef } & S 2 D e v & T \\\hline \text { Constant } & 32.6 & 19.3 & 1.689 \\x & 5.96 & 2.41 & 2.473 \\x ^ { 2 } & - 0.48 & 0.22 & - 2.182 \\\hline\end{array}$$ S = 16.1 R-Sq = 43.9%.
ANALYSIS OF VARIANCE $$\begin{array} { | l | c c c c | } \hline \text { Source of Variation } & d f & \text { SS } & \text { MS } & F \\\hline \text { Regression } & 2 & 3452 & 1726 & 6.663 \\\text { Error } & 17 & 4404 & 259.059 & \\\hline \text { Total } & 19 & 7856 & & \\\hline\end{array}$$ 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

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 59

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 60

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 = b₀ +b₁x.
b. Interpret the intercept.
c. Interpret the slope.

Question 61

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 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 5% significance level to conclude that income and experience are linearly related?

Question 63

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 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 economist is in the process of developing a model to predict the price of gold. She believes that the two most important variables are the price of a barrel of oil and the interest rate She proposes the first-order model with interaction: .
A random sample of 20 daily observations was taken. The computer output is shown below.
THE REGRESSION EQUATION IS Is there sufficient evidence at the 1% significance level to conclude that the price of a barrel of oil and the price of gold are linearly related?

Question 66

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 67

A professor of accounting wanted to develop a multiple regression model to predict the students' grades in her fourth-year accounting course. She decides that the two most important factors are the student's grade point average (GPA) in the first three years and the student's major. She proposes the model: .
where
y
= fourth-year accounting course mark (out of 100). = GPA in first three years (range 0 to 12). = 1 if student's major is accounting.
= 0 if not. = 1 if student's major is finance.
= 0 if not.
The computer output is shown below.
THE REGRESSION EQUATION IS . S = 15.0 R-Sq = 44.2%. Do these results allow us to conclude at the 1% significance level that on average finance majors outperform those whose majors are not accounting or finance?

Question 68

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

Question 70

An economist is in the process of developing a model to predict the price of gold. She believes that the two most important variables are the price of a barrel of oil and the interest rate She proposes the first-order model with interaction: .
A random sample of 20 daily observations was taken. The computer output is shown below.
THE REGRESSION EQUATION IS Is there sufficient evidence at the 1% significance level to conclude that the interest rate and the price of gold are linearly related?

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 What does the coefficient of tell you about the model?

Question 72

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 73

An economist is in the process of developing a model to predict the price of gold. She believes that the two most important variables are the price of a barrel of oil and the interest rate She proposes the first-order model with interaction: .
A random sample of 20 daily observations was taken. The computer output is shown below.
THE REGRESSION EQUATION IS . S = 20.9 R-Sq = 55.4%. Interpret the coefficient .

Question 74

An economist is in the process of developing a model to predict the price of gold. She believes that the two most important variables are the price of a barrel of oil and the interest rate She proposes the first-order model with interaction: .
A random sample of 20 daily observations was taken. The computer output is shown below.
THE REGRESSION EQUATION IS . S = 20.9 R-Sq = 55.4%. Do these results allow us at the 5% significance level to conclude that the model is useful in predicting the price of gold?

Question 75

An economist is in the process of developing a model to predict the price of gold. She believes that the two most important variables are the price of a barrel of oil and the interest rate She proposes the first-order model with interaction: . Is there sufficient evidence at the 1% significance level to conclude that the interaction term should be retained?

Question 76

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 77

A professor of accounting wanted to develop a multiple regression model to predict the students' grades in her fourth-year accounting course. She decides that the two most important factors are the student's grade point average (GPA) in the first three years and the student's major. She proposes the model: .
where
y
= fourth-year accounting course mark (out of 100). = GPA in first three years (range 0 to 12). = 1 if student's major is accounting.
= 0 if not. = 1 if student's major is finance.
= 0 if not.
The computer output is shown below.
THE REGRESSION EQUATION IS . S = 15.0 R-Sq = 44.2%. Do these results allow us to conclude at the 1% significance level that on average accounting majors outperform those whose majors are not accounting or finance?

Question 78

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 79

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 80

A professor of accounting wanted to develop a multiple regression model to predict the students' grades in her fourth-year accounting course. She decides that the two most important factors are the student's grade point average (GPA) in the first three years and the student's major. She proposes the model: .
where
y
= fourth-year accounting course mark (out of 100). = GPA in first three years (range 0 to 12). = 1 if student's major is accounting.
= 0 if not. = 1 if student's major is finance.
= 0 if not.
The computer output is shown below.
THE REGRESSION EQUATION IS . S = 15.0 R-Sq = 44.2%. Do these results allow us to conclude at the 1% significance level that the model is useful in predicting the fourth-year accounting course mark?