Deck 15: Multiple Regression Model Building

Question 1

A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. The business literature involving human capital shows that education influences an individual's annual income. Combined, these may influence family size. With this in mind, what should the real estate builder be particularly concerned with when analyzing the multiple regression model?

A) randomness of error terms
B) collinearity
C) normality of residuals
D) missing observations

Answer 1

collinearity

Question 2

As a project for his business statistics class, a student examined the factors that determined parking meter rates throughout the campus area. Data were collected for the price per hour of parking, blocks to the quadrangle, and one of the three jurisdictions: on campus, in downtown and off campus, or outside of downtown and off campus. The population regression model hypothesized is Y_i = α + β₀ + β₁X_1i + β₂X_2i + β₃X_3i + ε
Where
Y is the meter price
X₁ is the number of blocks to the quad
X₂ is a dummy variable that takes the value 1 if the meter is located in downtown and off campus and the value 0 otherwise
X₃ is a dummy variable that takes the value 1 if the meter is located outside of downtown and off campus, and the value 0 otherwise
Suppose that whether the meter is located on campus is an important explanatory factor. Why should the variable that depicts this attribute not be included in the model?

A) Its inclusion will introduce autocorrelation.
B) Its inclusion will introduce collinearity.
C) Its inclusion will inflate the standard errors of the estimated coefficients.
D) Both B and C.

Answer 2

Both B and C.

Question 3

TABLE 15-1
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
SUMMARY OUTPUT
Regression Statistics
ANOVA

Referring to Table 15-1, a more parsimonious simple linear model is likely to be statistically superior to the fitted curvilinear for predicting sale price (Y).

Answer 3

True

Question 4

TABLE 15-1
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
SUMMARY OUTPUT
Regression Statistics
ANOVA

Referring to Table 15-1, what is the p-value associated with the test statistic for testing whether there is an upward curvature in the response curve relating the demand (Y) and the price (X)?

A) 0.0001
B) 0.0006
C) 0.3647
D) None of the above.

Question 5

In multiple regression, the ________ procedure permits variables to enter and leave the model at different stages of its development.

A) forward selection
B) residual analysis
C) backward elimination
D) stepwise regression

Question 6

TABLE 15-1
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
SUMMARY OUTPUT
Regression Statistics
ANOVA

Referring to Table 15-1, what is the correct interpretation of the coefficient of multiple determination?

A) 98.8% of the total variation in demand can be explained by the linear relationship between demand and price.
B) 98.8% of the total variation in demand can be explained by the quadratic relationship between demand and price.
C) 98.8% of the total variation in demand can be explained by the addition of the square term in price.
D) 98.8% of the total variation in demand can be explained by just the square term in price.

Question 7

TABLE 15-2
In Hawaii, condemnation proceedings are under way to enable private citizens to own the property that their homes are built on. Until recently, only estates were permitted to own land, and homeowners leased the land from the estate. In order to comply with the new law, a large Hawaiian estate wants to use regression analysis to estimate the fair market value of the land. The following model was fit to data collected for n = 20 properties, 10 of which are located near a cove.
Using the data collected for the 20 properties, the following partial output obtained from Microsoft Excel is shown:
SUMMARY OUTPUT
Regression Statistics
ANOVA

Referring to Table 15-2, given a quadratic relationship between sale price (Y) and property size (X₁), what null hypothesis would you test to determine whether the curves differ from cove and non-cove properties?

A) H₀ : β₂ = β₃ = β₅ = 0
B) H₀ : β₄ = β₅ = 0
C) H₀ : β₃ = β₅ = 0
D) H₀ : β₂ = 0

Question 8

A regression diagnostic tool used to study the possible effects of collinearity is

A) the slope.
B) the Y-intercept.
C) the VIF.
D) the standard error of the estimate.

Question 9

TABLE 15-2
In Hawaii, condemnation proceedings are under way to enable private citizens to own the property that their homes are built on. Until recently, only estates were permitted to own land, and homeowners leased the land from the estate. In order to comply with the new law, a large Hawaiian estate wants to use regression analysis to estimate the fair market value of the land. The following model was fit to data collected for n = 20 properties, 10 of which are located near a cove.
Using the data collected for the 20 properties, the following partial output obtained from Microsoft Excel is shown:
SUMMARY OUTPUT
Regression Statistics
ANOVA

Referring to Table 15-2, given a quadratic relationship between sale price (Y) and property size (X₁), what test should be used to test whether the curves differ from cove and non-cove properties?

A) F test for the entire regression model.
B) t test on each of the coefficients in the entire regression model.
C) Partial F test on the subset of the appropriate coefficients.
D) t test on each of the subsets of the appropriate coefficients.

Question 10

The Variance Inflationary Factor (VIF) measures the correlation of the X variables with the Y variable.

Question 11

The Variance Inflationary Factor (VIF) measures the

A) correlation of the X variables with the Y variable.
B) correlation of the X variables with each other.
C) contribution of each X variable with the Y variable after all other X variables are included in the model.
D) standard deviation of the slope.

Question 12

TABLE 15-1
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
SUMMARY OUTPUT
Regression Statistics
ANOVA

Referring to Table 15-1, does there appear to be significant upward curvature in the response curve relating the demand (Y) and the price (X) at 10% level of significance?

A) Yes, since the p-value for the test is less than 0.10.
B) No, since the value of β₂ is near 0.
C) No, since the p-value for the test is greater than 0.10.
D) Yes, since the value of β₂ is positive.

Question 13

The C_p statistic is used

A) to determine if there is a problem of collinearity.
B) if the variances of the error terms are all the same in a regression model.
C) to choose the best model.
D) to determine if there is an irregular component in a time series.

Question 14

TABLE 15-2
In Hawaii, condemnation proceedings are under way to enable private citizens to own the property that their homes are built on. Until recently, only estates were permitted to own land, and homeowners leased the land from the estate. In order to comply with the new law, a large Hawaiian estate wants to use regression analysis to estimate the fair market value of the land. The following model was fit to data collected for n = 20 properties, 10 of which are located near a cove.
Using the data collected for the 20 properties, the following partial output obtained from Microsoft Excel is shown:
SUMMARY OUTPUT
Regression Statistics
ANOVA

Referring to Table 15-2, is the overall model statistically adequate at a 0.05 level of significance for predicting sale price (Y)?

A) No, since some of the t tests for the individual variables are not significant.
B) No, since the standard deviation of the model is fairly large.
C) Yes, since none of the β-estimates are equal to 0.
D) Yes, since the p-value for the test is smaller than 0.05.

Question 15

Which of the following is used to find a "best" model?

A) odds ratio
B) Mallows' C_p
C) standard error of the estimate
D) SST

Question 16

If a group of independent variables are not significant individually but are significant as a group at a specified level of significance, this is most likely due to

A) autocorrelation.
B) the presence of dummy variables.
C) the absence of dummy variables.
D) collinearity.

Question 17

A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. A statistical analyst discovers that capital spending by corporations has a significant inverse relationship with wage spending. What should the microeconomist who developed this multiple regression model be particularly concerned with?

A) randomness of error terms
B) collinearity
C) normality of residuals
D) missing observations

Question 18

Collinearity is present when there is a high degree of correlation between independent variables.

Question 19

Collinearity is present when there is a high degree of correlation between the dependent variable and any of the independent variables.

Question 20

TABLE 15-1
A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model:
where Y = demand (in thousands) and X = retail price per carat.
This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below:
SUMMARY OUTPUT
Regression Statistics
ANOVA

Referring to Table 15-1, what is the value of the test statistic for testing whether there is an upward curvature in the response curve relating the demand (Y) and the price (X)?

A) -5.14
B) 0.95
C) 373
D) None of the above.

Question 21

TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
SUMMARY OUTPUT
Regression Statistics
ANOVA

Referring to Table 15-3, suppose the chemist decides to use a t test to determine if there is a significant difference between a curvilinear model without a linear term and a curvilinear model that includes a linear term. Using a level of significance of 0.05, she would decide that the curvilinear model should include a linear term.

Question 22

Two simple regression models were used to predict a single dependent variable. Both models were highly significant, but when the two independent variables were placed in the same multiple regression model for the dependent variable, R² did not increase substantially and the parameter estimates for the model were not significantly different from 0. This is probably an example of collinearity.

Question 23

TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
SUMMARY OUTPUT
Regression Statistics
ANOVA

Referring to Table 15-3, suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose. If she chooses to use a level of significance of 0.01 she would decide that there is a significant curvilinear relationship.

Question 24

TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
SUMMARY OUTPUT
Regression Statistics
ANOVA

Referring to Table 15-3, suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a curvilinear model that includes a linear term. If she used a level of significance of 0.02, she would decide that the linear model is sufficient.

Question 25

One of the consequences of collinearity in multiple regression is biased estimates on the slope coefficients.

Question 26

TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
SUMMARY OUTPUT
Regression Statistics
ANOVA

Referring to Table 15-3, suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose. The value of the test statistic is ________.

Question 27

Collinearity is present if the dependent variable is linearly related to one of the explanatory variables.

Question 28

TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
SUMMARY OUTPUT
Regression Statistics
ANOVA

Referring to Table 15-3, suppose the chemist decides to use a t test to determine if there is a significant difference between a curvilinear model without a linear term and a curvilinear model that includes a linear term. The p-value of the test is ________.

Question 29

One of the consequences of collinearity in multiple regression is inflated standard errors in some or all of the estimated slope coefficients.

Question 30

The parameter estimates are biased when collinearity is present in a multiple regression equation.

Question 31

TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
SUMMARY OUTPUT
Regression Statistics
ANOVA

Referring to Table 15-3, suppose the chemist decides to use a t test to determine if there is a significant difference between a curvilinear model without a linear term and a curvilinear model that includes a linear term. The value of the test statistic is ________.

Question 32

TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
SUMMARY OUTPUT
Regression Statistics
ANOVA

Referring to Table 15-3, suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a curvilinear model that includes a linear term. If she used a level of significance of 0.05, she would decide that the linear model is sufficient.

Question 33

So that we can fit curves as well as lines by regression, we often use mathematical manipulations for converting one variable into a different form. These manipulations are called dummy variables.

Question 34

TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
SUMMARY OUTPUT
Regression Statistics
ANOVA

Referring to Table 15-3, the prediction of time to relief for a person receiving a dose of the drug 10 units above the average dose , is ________.

Question 35

In multiple regression, the ________ procedure permits variables to enter and leave the model at different stages of its development.

Question 36

TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
SUMMARY OUTPUT
Regression Statistics
ANOVA

Referring to Table 15-3, suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a curvilinear model that includes a linear term. The p-value of the test statistic for the contribution of the curvilinear term is ________.

Question 37

A high value of R² significantly above 0 in multiple regression accompanied by insignificant t-values on all parameter estimates very often indicates a high correlation between independent variables in the model.

Question 38

TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
SUMMARY OUTPUT
Regression Statistics
ANOVA

Referring to Table 15-3, suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose. The p-value of the test is ________.

Question 39

Collinearity will result in excessively low standard errors of the parameter estimates reported in the regression output.

Question 40

TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial containing a dose (X) of the drug and recorded the time to relief (Y) measured in seconds for each. She fit a "centered" curvilinear model to this data. The results obtained by Microsoft Excel follow, where the dose (X) given has been "centered."
SUMMARY OUTPUT
Regression Statistics
ANOVA

Referring to Table 15-3, suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose. If she chooses to use a level of significance of 0.05, she would decide that there is a significant curvilinear relationship.

Question 41

TABLE 15-4
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Let Y = % Passing as the dependent variable, X₁ = % Attendance, X₂ = Salaries and X₃ = Spending.
The coefficient of multiple determination (R_j ²) of each of the 3 predictors with all the other remaining predictors are, respectively, 0.0338, 0.4669, and 0.4743.
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):

Referring to Table 15-4, what are, respectively, the values of the variance inflationary factor of the 3 predictors?

Question 42

In stepwise regression, an independent variable is not allowed to be removed from the model once it has entered into the model.

Question 43

An independent variable X_j is considered highly correlated with the other independent variables if

A) VIF_j < 5.
B) VIF_j > 5.
C) VIF_j < VIF_i for i ≠ j.
D) VIF_j > VIF_i for i ≠ j.

Question 44

TABLE 15-4
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Let Y = % Passing as the dependent variable, X₁ = % Attendance, X₂ = Salaries and X₃ = Spending.
The coefficient of multiple determination (R_j ²) of each of the 3 predictors with all the other remaining predictors are, respectively, 0.0338, 0.4669, and 0.4743.
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):

Referring to Table 15-4, which of the following models should be taken into consideration using the Mallows' C_p statistic?

A) X₁, X₃
B) X₁, X₂, X₃
C) Both of the above.
D) None of the above.

Question 45

TABLE 15-4
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Let Y = % Passing as the dependent variable, X₁ = % Attendance, X₂ = Salaries and X₃ = Spending.
The coefficient of multiple determination (R_j ²) of each of the 3 predictors with all the other remaining predictors are, respectively, 0.0338, 0.4669, and 0.4743.
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):

Referring to Table 15-4, the "best" model using a 5% level of significance among those chosen by the C_p statistic is

A) X₁, X₃
B) X₁, X₂, X₃
C) Either of the above.
D) None of the above.

Question 46

In data mining where huge data sets are being explored to discover relationships among a large number of variables, the best-subsets approach is more practical than the stepwise regression approach.

Question 47

The logarithm transformation can be used

A) to overcome violations to the autocorrelation assumption.
B) to test for possible violations to the autocorrelation assumption.
C) to change a nonlinear model into a linear model.
D) to change a linear independent variable into a nonlinear independent variable.

Question 48

TABLE 15-4
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Let Y = % Passing as the dependent variable, X₁ = % Attendance, X₂ = Salaries and X₃ = Spending.
The coefficient of multiple determination (R_j ²) of each of the 3 predictors with all the other remaining predictors are, respectively, 0.0338, 0.4669, and 0.4743.
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):

Referring to Table 15-4, there is reason to suspect collinearity between some pairs of predictors.

Question 49

A regression diagnostic tool used to study the possible effects of collinearity is ________.

Question 50

TABLE 15-4
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Let Y = % Passing as the dependent variable, X₁ = % Attendance, X₂ = Salaries and X₃ = Spending.
The coefficient of multiple determination (R_j ²) of each of the 3 predictors with all the other remaining predictors are, respectively, 0.0338, 0.4669, and 0.4743.
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):

Referring to Table 15-4, the "best" model chosen using the adjusted R-square statistic is

A) X₁, X₃
B) X₁, X₂, X₃
C) Either of the above.
D) None of the above.

Question 51

The goals of model building are to find a good model with the fewest independent variables that is easier to interpret and has lower probability of collinearity.

Question 52

TABLE 15-4
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Let Y = % Passing as the dependent variable, X₁ = % Attendance, X₂ = Salaries and X₃ = Spending.
The coefficient of multiple determination (R_j ²) of each of the 3 predictors with all the other remaining predictors are, respectively, 0.0338, 0.4669, and 0.4743.
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):

Referring to Table 15-4, the residual plot suggests that a nonlinear model on % attendance may be a better model.

Question 53

The stepwise regression approach takes into consideration all possible models.

Question 54

TABLE 15-4
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Let Y = % Passing as the dependent variable, X₁ = % Attendance, X₂ = Salaries and X₃ = Spending.
The coefficient of multiple determination (R_j ²) of each of the 3 predictors with all the other remaining predictors are, respectively, 0.0338, 0.4669, and 0.4743.
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):

Referring to Table 15-4, the better model using a 5% level of significance derived from the "best" model above is

A) X₁
B) X₃
C) X₁, X₃
D) X₁, X₂, X₃

Question 55

Using the C_p statistic in model building, all models with C_p ≤ (k + 1) are equally good.

Question 56

TABLE 15-4
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Let Y = % Passing as the dependent variable, X₁ = % Attendance, X₂ = Salaries and X₃ = Spending.
The coefficient of multiple determination (R_j ²) of each of the 3 predictors with all the other remaining predictors are, respectively, 0.0338, 0.4669, and 0.4743.
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):

Referring to Table 15-4, which of the following predictors should first be dropped to remove collinearity?

A) X₁
B) X₂
C) X₃
D) None of the above.

Question 57

The ________ (larger/smaller) the value of the Variance Inflationary Factor, the higher is the collinearity of the X variables.

Question 58

Which of the following will NOT change a nonlinear model into a linear model?

A) quadratic regression model
B) logarithmic transformation
C) square-root transformation
D) variance inflationary factor

Question 59

The logarithm transformation can be used

A) to overcome violations to the autocorrelation assumption.
B) to test for possible violations to the autocorrelation assumption.
C) to overcome violations to the homoscedasticity assumption.
D) to test for possible violations to the homoscedasticity assumption.

Question 60

Using the best-subsets approach to model building, models are being considered when their

A) C_p > k.
B) C_p ≤ k.
C) C_p > (k + 1).
D) C_p ≤ (k + 1).

Question 61

TABLE 15-5
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below.
ANOVA
The various residual plots are as shown below.
The coefficient of partial determination ( ) of each of the 5 predictors are, respectively, 0.0380, 0.4376, 0.0248, 0.0188, and 0.0312.
The coefficient of multiple determination for the regression model using each of the 5 variables as the dependent variable and all other X variables as independent variables ( ) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, what is the correct interpretation for the estimated coefficient for Cargo Vol?

A) As the 0 to 60 miles per hour acceleration time increases by one second, the mean cargo volume will increase by an estimated 0.0259 cubic foot without taking into consideration all the other independent variables included in the model.
B) As the cargo volume increases by one cubic foot, the mean 0 to 60 miles per hour acceleration time will increase by an estimated 0.0259 seconds without taking into consideration all the other independent variables included in the model.
C) As the 0 to 60 miles per hour acceleration time increases by one second, the mean cargo volume will increase by an estimated 0.0259 cubic foot taking into consideration all the other independent variables included in the model.
D) As the cargo volume increases by one cubic foot, the mean 0 to 60 miles per hour acceleration time will increase by an estimated 0.0259 seconds taking into consideration all the other independent variables included in the model.

Question 62

TABLE 15-5
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below.
ANOVA
The various residual plots are as shown below.
The coefficient of partial determination ( ) of each of the 5 predictors are, respectively, 0.0380, 0.4376, 0.0248, 0.0188, and 0.0312.
The coefficient of multiple determination for the regression model using each of the 5 variables as the dependent variable and all other X variables as independent variables ( ) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, the 0 to 60 miles per hour acceleration time of a coupe is predicted to be 0.6427 seconds lower than that of a sedan.

Question 63

TABLE 15-5
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below.
ANOVA
The various residual plots are as shown below.
The coefficient of partial determination ( ) of each of the 5 predictors are, respectively, 0.0380, 0.4376, 0.0248, 0.0188, and 0.0312.
The coefficient of multiple determination for the regression model using each of the 5 variables as the dependent variable and all other X variables as independent variables ( ) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, what is the correct interpretation for the estimated coefficient for Sedan?

A) The mean 0 to 60 miles per hour acceleration time of a sedan is estimated to be 0.6427 seconds higher than that of a coupe after considering the effect of all the other independent variables in the model.
B) The mean 0 to 60 miles per hour acceleration time of a sedan is estimated to be 0.6427 seconds higher than that of an SUV after considering the effect of all the other independent variables in the model.
C) The mean 0 to 60 miles per hour acceleration time of a sedan is estimated to be 0.6427 seconds lower than that of a coupe after considering the effect of all the other independent variables in the model.
D) The mean 0 to 60 miles per hour acceleration time of a sedan is estimated to be 0.6427 seconds lower than that of an SUV after considering the effect of all the other independent variables in the model.

Question 64

TABLE 15-5
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below.
ANOVA
The various residual plots are as shown below.
The coefficient of partial determination ( ) of each of the 5 predictors are, respectively, 0.0380, 0.4376, 0.0248, 0.0188, and 0.0312.
The coefficient of multiple determination for the regression model using each of the 5 variables as the dependent variable and all other X variables as independent variables ( ) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, what is the correct interpretation for the estimated coefficient for HP?

A) As the horsepower increases by one unit, the mean 0 to 60 miles per hour acceleration time will decrease by an estimated 0.0200 seconds without taking into consideration all the other independent variables included in the model.
B) As the 0 to 60 miles per hour acceleration time increases by one second, the mean horsepower will decrease by an estimated 0.0200 unit without taking into consideration all the other independent variables included in the model.
C) As the horsepower increases by one unit, the mean 0 to 60 miles per hour acceleration time will decrease by an estimated 0.0200 seconds taking into consideration all the other independent variables included in the model.
D) As the 0 to 60 miles per hour acceleration time increases by one second, the mean horsepower will decrease by an estimated 0.0200 unit taking into consideration all the other independent variables included in the model.

Question 65

TABLE 15-5
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below.
ANOVA
The various residual plots are as shown below.
The coefficient of partial determination ( ) of each of the 5 predictors are, respectively, 0.0380, 0.4376, 0.0248, 0.0188, and 0.0312.
The coefficient of multiple determination for the regression model using each of the 5 variables as the dependent variable and all other X variables as independent variables ( ) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, what is the p-value of the test statistic to determine whether Cargo Vol makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?

Question 66

TABLE 15-5
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below.
ANOVA
The various residual plots are as shown below.
The coefficient of partial determination ( ) of each of the 5 predictors are, respectively, 0.0380, 0.4376, 0.0248, 0.0188, and 0.0312.
The coefficient of multiple determination for the regression model using each of the 5 variables as the dependent variable and all other X variables as independent variables ( ) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, the 0 to 60 miles per hour acceleration time of a sedan is predicted to be 0.7679 seconds higher than that of an SUV.

Question 67

TABLE 15-5
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below.
ANOVA
The various residual plots are as shown below.
The coefficient of partial determination ( ) of each of the 5 predictors are, respectively, 0.0380, 0.4376, 0.0248, 0.0188, and 0.0312.
The coefficient of multiple determination for the regression model using each of the 5 variables as the dependent variable and all other X variables as independent variables ( ) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, the 0 to 60 miles per hour acceleration time of a sedan is predicted to be 0.6427 seconds higher than that of an SUV.

Question 68

TABLE 15-5
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below.
ANOVA
The various residual plots are as shown below.
The coefficient of partial determination ( ) of each of the 5 predictors are, respectively, 0.0380, 0.4376, 0.0248, 0.0188, and 0.0312.
The coefficient of multiple determination for the regression model using each of the 5 variables as the dependent variable and all other X variables as independent variables ( ) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, the 0 to 60 miles per hour acceleration time of an SUV is predicted to be 0.1252 seconds higher than that of a sedan.

Question 69

TABLE 15-5
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below.
ANOVA
The various residual plots are as shown below.
The coefficient of partial determination ( ) of each of the 5 predictors are, respectively, 0.0380, 0.4376, 0.0248, 0.0188, and 0.0312.
The coefficient of multiple determination for the regression model using each of the 5 variables as the dependent variable and all other X variables as independent variables ( ) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, what is the correct interpretation for the estimated coefficient for SUV?

A) The mean 0 to 60 miles per hour acceleration time of an SUV is estimated to be 0.7679 seconds higher than that of a coupe after considering the effect of all the other independent variables in the model.
B) The mean 0 to 60 miles per hour acceleration time of an SUV is estimated to be 0.7679 seconds higher than that of a sedan after considering the effect of all the other independent variables in the model.
C) The mean 0 to 60 miles per hour acceleration time of an SUV is estimated to be 0.7679 seconds lower than that of a coupe after considering the effect of all the other independent variables in the model.
D) The mean 0 to 60 miles per hour acceleration time of an SUV is estimated to be 0.7679 seconds lower than that of a sedan after considering the effect of all the other independent variables in the model.

Question 70

TABLE 15-5
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below.
ANOVA
The various residual plots are as shown below.
The coefficient of partial determination ( ) of each of the 5 predictors are, respectively, 0.0380, 0.4376, 0.0248, 0.0188, and 0.0312.
The coefficient of multiple determination for the regression model using each of the 5 variables as the dependent variable and all other X variables as independent variables ( ) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, the 0 to 60 miles per hour acceleration time of a coupe is predicted to be 0.7679 seconds lower than that of an SUV.

Question 71

TABLE 15-5
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below.
ANOVA
The various residual plots are as shown below.
The coefficient of partial determination ( ) of each of the 5 predictors are, respectively, 0.0380, 0.4376, 0.0248, 0.0188, and 0.0312.
The coefficient of multiple determination for the regression model using each of the 5 variables as the dependent variable and all other X variables as independent variables ( ) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, the 0 to 60 miles per hour acceleration time of a coupe is predicted to be 0.7679 seconds higher than that of a sedan.

Question 72

TABLE 15-4
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Let Y = % Passing as the dependent variable, X₁ = % Attendance, X₂ = Salaries and X₃ = Spending.
The coefficient of multiple determination (R_j ²) of each of the 3 predictors with all the other remaining predictors are, respectively, 0.0338, 0.4669, and 0.4743.
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):

Referring to Table 15-4, what is the p-value of the test statistic to determine whether the quadratic effect of daily average of the percentage of students attending class on percentage of students passing the proficiency test is significant at a 5% level of significance?

Question 73

TABLE 15-5
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below.
ANOVA
The various residual plots are as shown below.
The coefficient of partial determination ( ) of each of the 5 predictors are, respectively, 0.0380, 0.4376, 0.0248, 0.0188, and 0.0312.
The coefficient of multiple determination for the regression model using each of the 5 variables as the dependent variable and all other X variables as independent variables ( ) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, what is the value of the test statistic to determine whether HP makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?

Question 74

TABLE 15-5
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below.
ANOVA
The various residual plots are as shown below.
The coefficient of partial determination ( ) of each of the 5 predictors are, respectively, 0.0380, 0.4376, 0.0248, 0.0188, and 0.0312.
The coefficient of multiple determination for the regression model using each of the 5 variables as the dependent variable and all other X variables as independent variables ( ) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, there is enough evidence to conclude that Cargo Vol makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance.

Question 75

TABLE 15-5
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below.
ANOVA
The various residual plots are as shown below.
The coefficient of partial determination ( ) of each of the 5 predictors are, respectively, 0.0380, 0.4376, 0.0248, 0.0188, and 0.0312.
The coefficient of multiple determination for the regression model using each of the 5 variables as the dependent variable and all other X variables as independent variables ( ) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, the 0 to 60 miles per hour acceleration time of a sedan is predicted to be 0.1252 seconds higher than that of an SUV.

Question 76

TABLE 15-5
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below.
ANOVA
The various residual plots are as shown below.
The coefficient of partial determination ( ) of each of the 5 predictors are, respectively, 0.0380, 0.4376, 0.0248, 0.0188, and 0.0312.
The coefficient of multiple determination for the regression model using each of the 5 variables as the dependent variable and all other X variables as independent variables ( ) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, what is the value of the test statistic to determine whether Cargo Vol makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?

Question 77

TABLE 15-4
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Let Y = % Passing as the dependent variable, X₁ = % Attendance, X₂ = Salaries and X₃ = Spending.
The coefficient of multiple determination (R_j ²) of each of the 3 predictors with all the other remaining predictors are, respectively, 0.0338, 0.4669, and 0.4743.
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):

Referring to Table 15-4, the null hypothesis should be rejected when testing whether the quadratic effect of daily average of the percentage of students attending class on percentage of students passing the proficiency test is significant at a 5% level of significance.

Question 78

TABLE 15-5
What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu. ft.
HP: Horsepower
MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0
Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below.
ANOVA
The various residual plots are as shown below.
The coefficient of partial determination ( ) of each of the 5 predictors are, respectively, 0.0380, 0.4376, 0.0248, 0.0188, and 0.0312.
The coefficient of multiple determination for the regression model using each of the 5 variables as the dependent variable and all other X variables as independent variables ( ) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.
Referring to Table 15-5, what is the correct interpretation for the estimated coefficient for MPG?

A) As the miles per gallon decreases by one unit, the mean 0 to 60 miles per hour acceleration time will increase by an estimated 0.0620 seconds without taking into consideration all the other independent variables included in the model.
B) As the 0 to 60 miles per hour acceleration time decreases by one second, the mean miles per gallon will increase by an estimated 0.0620 unit without taking into consideration all the other independent variables included in the model.
C) As the miles per gallon decreases by one unit, the mean 0 to 60 miles per hour acceleration time will increase by an estimated 0.0620 seconds taking into consideration all the other independent variables included in the model.
D) As the 0 to 60 miles per hour acceleration time decreases by one second, the mean miles per gallon will increase by an estimated 0.0620 unit taking into consideration all the other independent variables included in the model.

Question 79

TABLE 15-4
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Let Y = % Passing as the dependent variable, X₁ = % Attendance, X₂ = Salaries and X₃ = Spending.
The coefficient of multiple determination (R_j ²) of each of the 3 predictors with all the other remaining predictors are, respectively, 0.0338, 0.4669, and 0.4743.
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):

Referring to Table 15-4, the quadratic effect of daily average of the percentage of students attending class on percentage of students passing the proficiency test is not significant at a 5% level of significance.

Question 80

TABLE 15-4
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.
Let Y = % Passing as the dependent variable, X₁ = % Attendance, X₂ = Salaries and X₃ = Spending.
The coefficient of multiple determination (R_j ²) of each of the 3 predictors with all the other remaining predictors are, respectively, 0.0338, 0.4669, and 0.4743.
The output from the best-subset regressions is given below:
Following is the residual plot for % Attendance:
Following is the output of several multiple regression models:
Model (I):
Model (II):
Model (III):

Referring to Table 15-4, what is the value of the test statistic to determine whether the quadratic effect of daily average of the percentage of students attending class on percentage of students passing the proficiency test is significant at a 5% level of significance?