Deck 15: Multiple Regression

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 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

Answer 1

B

Question 2

SCENARIO 15-2

Answer 2

C

Question 3

SCENARIO 15-2
Referring to Scenario 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.

Answer 3

C

Question 4

SCENARIO 15-1
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 5

True or False: Collinearity is present when there is a high degree of correlation between
independent variables.

Question 6

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 7

SCENARIO 15-1
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 8

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

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

Question 9

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 10

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 11

SCENARIO 15-1
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 12

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

Question 13

SCENARIO 15-1

Question 14

SCENARIO 15-1
True or False: 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 15

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.

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

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

Question 18

Question 19

SCENARIO 15-2

Question 20

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 21

Question 22

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

Question 23

True or False: 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 24

SCENARIO 15-4
15-16 Multiple Regression Model Building
Referring to Scenario 15-4, what are, respectively, the values of the variance inflationary factor of
the 3 predictors?

Question 25

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 26

True or False: Collinearity is present if the dependent variable is linearly related to one of the
explanatory variables.

Question 27

True or False: One of the consequences of collinearity in multiple regression is biased estimates
on the slope coefficients.

Question 28

Question 29

True or False: The parameter estimates are biased when collinearity is present in a multiple
regression equation.

Question 30

Question 31

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 32

Question 33

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

Question 34

True or False: 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 35

True or False: The stepwise regression approach takes into consideration all possible models.

Question 36

True or False: 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 37

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 38

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 39

True or False: 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 40

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

Question 41

SCENARIO 15-4
15-16 Multiple Regression Model Building

Question 42

SCENARIO 15-4
15-16 Multiple Regression Model Building

Question 43

SCENARIO 15-4
15-16 Multiple Regression Model Building
True or False: Referring to Scenario 15-4, the residual plot suggests that a nonlinear model on %
attendance may be a better model.

Question 44

SCENARIO 15-4
15-16 Multiple Regression Model Building
True or False: Referring to Scenario 15-4, there is reason to suspect collinearity between some
pairs of predictors.

Question 45

SCENARIO 15-4
15-16 Multiple Regression Model Building

Question 46

SCENARIO 15-6
True or False: Referring to Scenario 15-6, the variable
should be dropped to remove
collinearity?

Question 47

SCENARIO 15-4
15-16 Multiple Regression Model Building

Question 48

SCENARIO 15-6
True or False: Referring to Scenario 15-6, the variable
should be dropped to remove
collinearity?

Question 49

Question 50

SCENARIO 15-6
True or False: Referring to Scenario 15-6, the variable
should be dropped to remove
collinearity?

Question 51

Question 52

SCENARIO 15-4
15-16 Multiple Regression Model Building

Question 53

SCENARIO 15-6
True or False: 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 54

SCENARIO 15-6
True or False: Referring to Scenario 15-6, the variable
should be dropped to remove
collinearity?

Question 55

SCENARIO 15-6
True or False: Referring to Scenario 15-6, the variable
should be dropped to remove
collinearity?

Question 56

.

Question 57

SCENARIO 15-6
True or False: Referring to Scenario 15-6, the variable
should be dropped to remove
collinearity?

Question 58

Question 59

Question 60

Question 61

Question 62