Deck 15: Multiple Regression

Question 1

The Cp 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.

Answer 1

C

Question 2

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.

Answer 2

B

Question 3

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.

Answer 3

True

Question 4

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 constructed the multiple regression
Model. 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

Question 5

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 6

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 7

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

Question 8

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

Question 9

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

Question 10

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

A) Odds ratio
B) Mallow's Cp
C) Standard error of the estimate
D) SST

Question 11

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

Question 12

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 13

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

Question 14

SCENARIO 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: $Y = \beta _ { 0 } + \beta _ { 1 } X + \beta _ { 2 } X ^ { 2 } + \varepsilon$ 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:

-Referring to Scenario 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 15

SCENARIO 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: $Y = \beta _ { 0 } + \beta _ { 1 } X + \beta _ { 2 } X ^ { 2 } + \varepsilon$ 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:

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

Question 16

SCENARIO 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. Model 1: $Y = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 2 } + \beta _ { 3 } X _ { 1 } X _ { 2 } + \beta _ { 4 } X _ { 1 } ^ { 2 } + \beta _ { 5 } X _ { 1 } ^ { 2 } X _ { 2 } + \varepsilon$
where $Y =$ Sale price of property in thousands of dollars
$X _ { 1 } =$ Size of property in thousands of square feet
$X _ { 2 } = 1$ if property located near cove, 0 if not Using the data collected for the 20 properties, the following partial output obtained from Microsoft
Excel is shown:

-Referring to Scenario 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 ?-estimates are equal to 0.
D) Yes, since the p-value for the test is smaller than 0.05.

Question 17

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 18

SCENARIO 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. Model 1: $Y = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 2 } + \beta _ { 3 } X _ { 1 } X _ { 2 } + \beta _ { 4 } X _ { 1 } ^ { 2 } + \beta _ { 5 } X _ { 1 } ^ { 2 } X _ { 2 } + \varepsilon$
where $Y =$ Sale price of property in thousands of dollars
$X _ { 1 } =$ Size of property in thousands of square feet
$X _ { 2 } = 1$ if property located near cove, 0 if not Using the data collected for the 20 properties, the following partial output obtained from Microsoft
Excel is shown:

-Referring to Scenario 15-2, given a quadratic relationship between sale price (Y) and property size ( $X _ { 1 }$ ), 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 19

SCENARIO 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: $Y = \beta _ { 0 } + \beta _ { 1 } X + \beta _ { 2 } X ^ { 2 } + \varepsilon$ 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:

-Referring to Scenario 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 20

SCENARIO 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: $Y = \beta _ { 0 } + \beta _ { 1 } X + \beta _ { 2 } X ^ { 2 } + \varepsilon$ 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:

-Referring to Scenario 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 21

SCENARIO 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 curvilinear model
to this data. The results obtained by Microsoft Excel follow
Referring to Scenario 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 22

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

Question 23

SCENARIO 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 curvilinear model
to this data. The results obtained by Microsoft Excel follow
Referring to Scenario 15-3, the prediction of time to relief for a person receiving a dose of 10
units of the drug is ________.

Question 24

SCENARIO 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 curvilinear model
to this data. The results obtained by Microsoft Excel follow
Referring to Scenario 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 25

SCENARIO 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 curvilinear model
to this data. The results obtained by Microsoft Excel follow
Referring to Scenario 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 26

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

Question 27

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

Question 28

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

Question 29

SCENARIO 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 curvilinear model
to this data. The results obtained by Microsoft Excel follow
Referring to Scenario 15-3, suppose the chemist decides to use a t test to determine
if the linear term is significant. Using a level of significance of 0.05, she would decide that the
linear term is significant.

Question 30

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 31

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 32

SCENARIO 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 curvilinear model
to this data. The results obtained by Microsoft Excel follow
Referring to Scenario 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 0.01, 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

SCENARIO 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 curvilinear model
to this data. The results obtained by Microsoft Excel follow
Referring to Scenario 15-3, suppose the chemist decides to use a t test to determine if the linear
term is significant. The p-value of the test is ______.

Question 35

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

Question 36

SCENARIO 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 curvilinear model
to this data. The results obtained by Microsoft Excel follow
Referring to Scenario 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 37

SCENARIO 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 curvilinear model
to this data. The results obtained by Microsoft Excel follow
Referring to Scenario 15-3, suppose the chemist decides to use a t test to determine if the linear
term is significant. The value of the test statistic is ______.

Question 38

SCENARIO 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 curvilinear model
to this data. The results obtained by Microsoft Excel follow
Referring to Scenario 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 39

SCENARIO 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 curvilinear model
to this data. The results obtained by Microsoft Excel follow
Referring to Scenario 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 40

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

Question 41

SCENARIO 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 mean of the percentage of students attending class (% Attendance), mean teacher
salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in
the state.
Referring to Scenario 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 42

SCENARIO 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 mean of the percentage of students attending class (% Attendance), mean teacher
salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in
the state.
Referring to Scenario 15-4, what are, respectively, the values of the variance inflationary factor of
the 3 predictors?

Question 43

The stepwise regression approach takes into consideration all possible models.

Question 44

SCENARIO 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 mean of the percentage of students attending class (% Attendance), mean teacher
salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in
the state.
Referring to Scenario 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 45

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 46

SCENARIO 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 mean of the percentage of students attending class (% Attendance), mean teacher
salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in
the state.
Referring to Scenario 15-4, there is reason to suspect collinearity between some
pairs of predictors.

Question 47

SCENARIO 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 mean of the percentage of students attending class (% Attendance), mean teacher
salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in
the state.
Referring to Scenario 15-4, the residual plot suggests that a nonlinear model on %
attendance may be a better model.

Question 48

Using the $$C _ { p } \text { statistic in model building, all models with } C _ { p } \leq ( k + 1 ) \text { are equally }$$ good.

Question 49

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

Question 50

SCENARIO 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 mean of the percentage of students attending class (% Attendance), mean teacher
salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in
the state.
Referring to Scenario 15-4, the better model using a 5% level of significance derived from the "best" model above is

Question 51

SCENARIO 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 mean of the percentage of students attending class (% Attendance), mean teacher
salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in
the state.
Referring to Scenario 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?

Question 52

SCENARIO 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
Referring to Scenario 15-5, what is the value of the variance inflationary factor of Cargo Vol?

Question 53

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

Question 54

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 55

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 56

SCENARIO 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 mean of the percentage of students attending class (% Attendance), mean teacher
salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in
the state.
Referring to Scenario 15-4, which of the following predictors should first be dropped to remove collinearity?

Question 57

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 58

SCENARIO 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 mean of the percentage of students attending class (% Attendance), mean teacher
salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in
the state.
Referring to Scenario 15-4, the "best" model chosen using the adjusted R-square statistic is

Question 59

SCENARIO 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
Referring to Scenario 15-5, what is the value of the variance inflationary factor of HP?

Question 60

SCENARIO 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 mean of the percentage of students attending class (% Attendance), mean teacher
salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in
the state.
Referring to Scenario 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 61

SCENARIO 15-6 Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff $( Y )$ and the independent variables are the age of the worker $\left( X _ { 1 } \right)$ , the number of years of education received $\left( X _ { 2 } \right)$ , the number of years at the previous job $\left( X _ { 3 } \right)$ , a dummy variable for marital status ( $X _ { 4 } : 1 =$ married, $0 =$ otherwise), a dummy variable for head of household $\left( X _ { 5 } : 1 = \right.$ yes, $0 =$ no) and a dummy variable for management position $\left( X _ { 6 } : 1 = \right.$ yes, $0 =$ no $)$ .

The coefficient of multiple determination $\left( R _ { j } ^ { 2 } \right)$ for the regression model using each of the 6 variables $X _ { j }$ as the dependent variable and all other $X$ variables as independent variables are, respectively, $0.2628,0.1240,0.2404,0.3510,0.3342$ and $0.0993$ .

The partial results from best-subset regression are given below:
$\begin{array}{|l|r|r|r|}\hline {\text { Model }} & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5X6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \text { X1X2X5X6 } & 0.4697 & 0.4091 & 18.3919 \\\hline \text { X1X3X5X6 } & 0.4691 & 0.4084 & 18.4023 \\\hline \text { X1X2X3X5X6 } & 0.4877 & 0.4123 & 18.3416 \\\hline \text { X1X2X3X4X5X6 } & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$


-Referring to Scenario 15-6, the variable X3 should be dropped to remove
collinearity?

Question 62

SCENARIO 15-6 Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff $( Y )$ and the independent variables are the age of the worker $\left( X _ { 1 } \right)$ , the number of years of education received $\left( X _ { 2 } \right)$ , the number of years at the previous job $\left( X _ { 3 } \right)$ , a dummy variable for marital status ( $X _ { 4 } : 1 =$ married, $0 =$ otherwise), a dummy variable for head of household $\left( X _ { 5 } : 1 = \right.$ yes, $0 =$ no) and a dummy variable for management position $\left( X _ { 6 } : 1 = \right.$ yes, $0 =$ no $)$ .

The coefficient of multiple determination $\left( R _ { j } ^ { 2 } \right)$ for the regression model using each of the 6 variables $X _ { j }$ as the dependent variable and all other $X$ variables as independent variables are, respectively, $0.2628,0.1240,0.2404,0.3510,0.3342$ and $0.0993$ .

The partial results from best-subset regression are given below:
$\begin{array}{|l|r|r|r|}\hline {\text { Model }} & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5X6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \text { X1X2X5X6 } & 0.4697 & 0.4091 & 18.3919 \\\hline \text { X1X3X5X6 } & 0.4691 & 0.4084 & 18.4023 \\\hline \text { X1X2X3X5X6 } & 0.4877 & 0.4123 & 18.3416 \\\hline \text { X1X2X3X4X5X6 } & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$


-Referring to Scenario 15-6, the variable X2 should be dropped to remove
collinearity?

Question 63

SCENARIO 15-6 Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff $( Y )$ and the independent variables are the age of the worker $\left( X _ { 1 } \right)$ , the number of years of education received $\left( X _ { 2 } \right)$ , the number of years at the previous job $\left( X _ { 3 } \right)$ , a dummy variable for marital status ( $X _ { 4 } : 1 =$ married, $0 =$ otherwise), a dummy variable for head of household $\left( X _ { 5 } : 1 = \right.$ yes, $0 =$ no) and a dummy variable for management position $\left( X _ { 6 } : 1 = \right.$ yes, $0 =$ no $)$ .

The coefficient of multiple determination $\left( R _ { j } ^ { 2 } \right)$ for the regression model using each of the 6 variables $X _ { j }$ as the dependent variable and all other $X$ variables as independent variables are, respectively, $0.2628,0.1240,0.2404,0.3510,0.3342$ and $0.0993$ .

The partial results from best-subset regression are given below:
$\begin{array}{|l|r|r|r|}\hline {\text { Model }} & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5X6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \text { X1X2X5X6 } & 0.4697 & 0.4091 & 18.3919 \\\hline \text { X1X3X5X6 } & 0.4691 & 0.4084 & 18.4023 \\\hline \text { X1X2X3X5X6 } & 0.4877 & 0.4123 & 18.3416 \\\hline \text { X1X2X3X4X5X6 } & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$


-Referring to Scenario 15-6, the variable X1 should be dropped to remove
collinearity?

Question 64

SCENARIO 15-6
Referring to Scenario 15-6, what is the value of the variance inflationary factor of Job Yr?

Question 65

SCENARIO 15-6
Referring to Scenario 15-6, what is the value of the variance inflationary factor of Head?

Question 66

SCENARIO 15-6 Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff $( Y )$ and the independent variables are the age of the worker $\left( X _ { 1 } \right)$ , the number of years of education received $\left( X _ { 2 } \right)$ , the number of years at the previous job $\left( X _ { 3 } \right)$ , a dummy variable for marital status ( $X _ { 4 } : 1 =$ married, $0 =$ otherwise), a dummy variable for head of household $\left( X _ { 5 } : 1 = \right.$ yes, $0 =$ no) and a dummy variable for management position $\left( X _ { 6 } : 1 = \right.$ yes, $0 =$ no $)$ .

The coefficient of multiple determination $\left( R _ { j } ^ { 2 } \right)$ for the regression model using each of the 6 variables $X _ { j }$ as the dependent variable and all other $X$ variables as independent variables are, respectively, $0.2628,0.1240,0.2404,0.3510,0.3342$ and $0.0993$ .

The partial results from best-subset regression are given below:
$\begin{array}{|l|r|r|r|}\hline {\text { Model }} & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5X6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \text { X1X2X5X6 } & 0.4697 & 0.4091 & 18.3919 \\\hline \text { X1X3X5X6 } & 0.4691 & 0.4084 & 18.4023 \\\hline \text { X1X2X3X5X6 } & 0.4877 & 0.4123 & 18.3416 \\\hline \text { X1X2X3X4X5X6 } & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$


-Referring to Scenario 15-6, the variable X5 should be dropped to remove
collinearity?

Question 67

SCENARIO 15-6
Referring to Scenario 15-6, what is the value of the variance inflationary factor of Edu?

Question 68

SCENARIO 15-6
Referring to Scenario 15-6, what is the value of the variance inflationary factor of Manager?

Question 69

SCENARIO 15-6
Referring to Scenario 15-6, what is the value of the Mallow's statistic for the model that
includes all the six independent variables?

Question 70

SCENARIO 15-6 Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff $( Y )$ and the independent variables are the age of the worker $\left( X _ { 1 } \right)$ , the number of years of education received $\left( X _ { 2 } \right)$ , the number of years at the previous job $\left( X _ { 3 } \right)$ , a dummy variable for marital status ( $X _ { 4 } : 1 =$ married, $0 =$ otherwise), a dummy variable for head of household $\left( X _ { 5 } : 1 = \right.$ yes, $0 =$ no) and a dummy variable for management position $\left( X _ { 6 } : 1 = \right.$ yes, $0 =$ no $)$ .

The coefficient of multiple determination $\left( R _ { j } ^ { 2 } \right)$ for the regression model using each of the 6 variables $X _ { j }$ as the dependent variable and all other $X$ variables as independent variables are, respectively, $0.2628,0.1240,0.2404,0.3510,0.3342$ and $0.0993$ .

The partial results from best-subset regression are given below:
$\begin{array}{|l|r|r|r|}\hline {\text { Model }} & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5X6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \text { X1X2X5X6 } & 0.4697 & 0.4091 & 18.3919 \\\hline \text { X1X3X5X6 } & 0.4691 & 0.4084 & 18.4023 \\\hline \text { X1X2X3X5X6 } & 0.4877 & 0.4123 & 18.3416 \\\hline \text { X1X2X3X4X5X6 } & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$


-Referring to Scenario 15-6, the model that includes $X _ { 1 } , X _ { 5 } \text { and } X _ { 6 }$ should be among
the appropriate models using the Mallow's $C _ { p }$ statistic.

Question 71

SCENARIO 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
Referring to Scenario 15-5, what is the value of the variance inflationary factor of SUV?

Question 72

SCENARIO 15-6 Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff $( Y )$ and the independent variables are the age of the worker $\left( X _ { 1 } \right)$ , the number of years of education received $\left( X _ { 2 } \right)$ , the number of years at the previous job $\left( X _ { 3 } \right)$ , a dummy variable for marital status ( $X _ { 4 } : 1 =$ married, $0 =$ otherwise), a dummy variable for head of household $\left( X _ { 5 } : 1 = \right.$ yes, $0 =$ no) and a dummy variable for management position $\left( X _ { 6 } : 1 = \right.$ yes, $0 =$ no $)$ .

The coefficient of multiple determination $\left( R _ { j } ^ { 2 } \right)$ for the regression model using each of the 6 variables $X _ { j }$ as the dependent variable and all other $X$ variables as independent variables are, respectively, $0.2628,0.1240,0.2404,0.3510,0.3342$ and $0.0993$ .

The partial results from best-subset regression are given below:
$\begin{array}{|l|r|r|r|}\hline {\text { Model }} & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5X6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \text { X1X2X5X6 } & 0.4697 & 0.4091 & 18.3919 \\\hline \text { X1X3X5X6 } & 0.4691 & 0.4084 & 18.4023 \\\hline \text { X1X2X3X5X6 } & 0.4877 & 0.4123 & 18.3416 \\\hline \text { X1X2X3X4X5X6 } & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$


-Referring to Scenario 15-6, the variable X4 should be dropped to remove
collinearity?

Question 73

SCENARIO 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
Referring to Scenario 15-5, what is the value of the variance inflationary factor of MPG?

Question 74

SCENARIO 15-6 Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff $( Y )$ and the independent variables are the age of the worker $\left( X _ { 1 } \right)$ , the number of years of education received $\left( X _ { 2 } \right)$ , the number of years at the previous job $\left( X _ { 3 } \right)$ , a dummy variable for marital status ( $X _ { 4 } : 1 =$ married, $0 =$ otherwise), a dummy variable for head of household $\left( X _ { 5 } : 1 = \right.$ yes, $0 =$ no) and a dummy variable for management position $\left( X _ { 6 } : 1 = \right.$ yes, $0 =$ no $)$ .

The coefficient of multiple determination $\left( R _ { j } ^ { 2 } \right)$ for the regression model using each of the 6 variables $X _ { j }$ as the dependent variable and all other $X$ variables as independent variables are, respectively, $0.2628,0.1240,0.2404,0.3510,0.3342$ and $0.0993$ .

The partial results from best-subset regression are given below:
$\begin{array}{|l|r|r|r|}\hline {\text { Model }} & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5X6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \text { X1X2X5X6 } & 0.4697 & 0.4091 & 18.3919 \\\hline \text { X1X3X5X6 } & 0.4691 & 0.4084 & 18.4023 \\\hline \text { X1X2X3X5X6 } & 0.4877 & 0.4123 & 18.3416 \\\hline \text { X1X2X3X4X5X6 } & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$


-Referring to Scenario 15-6, the model that includes $X _ { 1 } , X _ { 2 } , X _ { 5 } \text { and } X _ { 6 }$ should be
among the appropriate models using the Mallow's $C _ { p }$ statistic.

Question 75

SCENARIO 15-6 Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff $( Y )$ and the independent variables are the age of the worker $\left( X _ { 1 } \right)$ , the number of years of education received $\left( X _ { 2 } \right)$ , the number of years at the previous job $\left( X _ { 3 } \right)$ , a dummy variable for marital status ( $X _ { 4 } : 1 =$ married, $0 =$ otherwise), a dummy variable for head of household $\left( X _ { 5 } : 1 = \right.$ yes, $0 =$ no) and a dummy variable for management position $\left( X _ { 6 } : 1 = \right.$ yes, $0 =$ no $)$ .

The coefficient of multiple determination $\left( R _ { j } ^ { 2 } \right)$ for the regression model using each of the 6 variables $X _ { j }$ as the dependent variable and all other $X$ variables as independent variables are, respectively, $0.2628,0.1240,0.2404,0.3510,0.3342$ and $0.0993$ .

The partial results from best-subset regression are given below:
$\begin{array}{|l|r|r|r|}\hline {\text { Model }} & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5X6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \text { X1X2X5X6 } & 0.4697 & 0.4091 & 18.3919 \\\hline \text { X1X3X5X6 } & 0.4691 & 0.4084 & 18.4023 \\\hline \text { X1X2X3X5X6 } & 0.4877 & 0.4123 & 18.3416 \\\hline \text { X1X2X3X4X5X6 } & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$


-Referring to Scenario 15-6, there is reason to suspect collinearity between some
pairs of predictors based on the values of the variance inflationary factor.

Question 76

SCENARIO 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
Referring to Scenario 15-5, what is the value of the variance inflationary factor of Sedan?

Question 77

SCENARIO 15-6
Referring to Scenario 15-6, what is the value of the variance inflationary factor of Married?

Question 78

SCENARIO 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 coefficient of multiple determination $\left( R _ { j } ^ { 2 } \right)$ for the regression model using each of the 5 variables $X _ { j }$ 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 Scenario 15-5, there is reason to suspect collinearity between some
pairs of predictors based on the values of the variance inflationary factor.

Question 79

SCENARIO 15-6
Referring to Scenario 15-6, the variable X6 should be dropped to remove
collinearity?

Question 80

SCENARIO 15-6
Referring to Scenario 15-6, what is the value of the variance inflationary factor of Age?