Principles of Econometrics 4th Edition by R. Carter Hill -Test Bank

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File:  Ch05, Chapter 5, The Multiple Regression Model

 

Multiple Choice

 

  1. When an error term is added to an economic model and assumptions about the distribution of the error term are made, the resulting model is ______________.

a.)  fallacious, you should not make assumptions about error terms.

b.)  an econometric model that can be estimated and used for inference.

c.)  misspecified due to missing information.

d.)  heteroskedastic since error terms are no longer random.

 

Ans:  b

Level:  Easy

Section:  5.1

 

 

 

2.)  How should bk in the general multiple regression model be interpreted?

a.)  The number of units of change in the expected value of y for a 1 unit increase in xk when all remaining variables are unchanged

b.)  the magnitude by which xk varies in the model

c.)  the amount of variation in y explained by xk in the model

d.)  the number of variables used in the model.

 

Ans:  a

Level:  Moderate

Section:  5.1

 

 

 

3.)  Which of the following is not an assumption of the multiple regression model?

a.)  The values of each xik are not random and are not exact linear functions of the other explanatory variables.

b.)  var(yi.) = var(ei) = s2

c.)  The least squares estimators are BLUE.

d.)  cov(yi, yj) = cov(ei, ej) = 0;    (i≠j)

 

Ans:  c

Level:  Moderate/Difficult

Section:  5.1

 

 

 

4.)  What is the unbiased estimator of s2 in the multiple regression model?

a.)

b.)

c.)

d.)

 

Ans:  c

Level:  Moderate/Difficult

Section:  5.2

 

 

 

5.)  Why does the denominator of ŝ2 need to be the same as the degrees of freedom in the model?

a.)  so we will know how the estimate is distributed if Ho is true

b.)  so we can extrapolate the results to other values of x

c.)  so that the root MSE will be a positive number

d.)  so the estimator will be unbiased

 

Ans:  d

Level:  Moderate

Section:  5.2

 

 

 

6.)  In the multiple regression model which of the following does NOT lead to larger variances of the least squares estimators b2 and var(b2)?

a.)  larger error variances, s2

b.)  larger correlation between x2 and x3

c.)  smaller values of Ʃ(xi2 – x̅2)2

d.)  larger correlation between x2 and y

 

Ans:  d

Level:  Difficult

Section:  5.3

 

 

 

7.)  The matrix below represents the variance-covariance matrix estimated from the multiple regression model:

Which 2 elements of the matrix should always be equal?

a.)  A & I

b.)  B & H

c.)  C & G

d.)  D & F

 

Ans:  c

Level:  Easy

Section:  5.3

 

 

 

8.)  The matrix below represents the variance-covariance matrix estimated from the multiple regression model:

Which element of the matrix cannot be negative?

a.)  A

b.)  B

c.)  C

d.)  D

 

Ans:  a

Level:  Moderate

Section:  5.3

 

 

 

9.)  You have estimated a multiple regression model with 6 explanatory variables and an intercept from a sample with 46 observations.  What is tc if you want to perform a right-tailed hypothesis test at the .01 level of significance?

a.)  2.426

b.)  2.708

c.)  2.423

d.)  2.704

 

Ans:  a

Level:  Easy

Section:  5.3

 

 

 

10.)  You estimate a model with 5 explanatory variables and an intercept from a data set with 247 observations.  To test hypotheses on this model you should use a t distribution with how many degrees of freedom?

a.)  242

b.)  120

c.)  ∞

d.)  241

 

Ans: d

Level:  Easy

Section:  5.3

 

 

 

  1. A model estimated using a dataset with 125 observations generates the following results.
Variable   b   Std. Error   t   P>|t|
x2 -0.01264 0.005519 -2.28937 0.022
x3 0.595792 0.014482 41.13934 0.000
x4 1.124589 0.877192 1.282032 0.200
x5 0.323742 0.060709 5.332661 0.000
Constant 8.86016 1.766116 5.016749 0.000
 

What are the endpoints for the 95% confidence interval for b3?

 

a.)(-0.6842, 1.8758)

b.)(-1.3842, 2.5758)

c.)(.5672, 6245)

d.)(-40.5435 , 41.7251)

 

Ans:  c

Level:  Moderate

Section:  5.4

 

 

 

 

12.)  A model estimated using a dataset with 65 observations generates the following results.

Variable   b   Std. Error   t   P>|t|
x2 -0.01264 0.005519 -2.28937 0.022
x3 0.595792 0.014482 41.13934 0.000
x4 1.124589 0.877192 1.282032 0.200
x5 0.323742 0.060709 5.332661 0.000
Constant 8.86016 1.766116 5.016749 0.000
 

What are the endpoints for the 99% confidence interval for b5?

 

a.)  (0.1623, 0.4852)

b.)  (-5.0089 , 5.6564)

c.)  (0.2630 , 0.3845)

d.)  (0.1786 , 0.4688)

 

Ans:  a

Level:  Moderate

Section:  5.4

 

 

 

14.)  A model estimated using a dataset with 65 observations generates the following results.

Variable   b   Std. Error   t   P>|t|
x2 -0.01264 0.005519 -2.28937 0.022
x3 0.595792 0.014482 41.13934 0.000
x4 1.124589 0.877192 1.282032 0.200
x5 0.323742 0.060709 5.332661 0.000
Constant 8.86016 1.766116 5.016749 0.000
 

 

If you want to test the hypothesis that b3 =0.45, what is the test statistic from this sample?

a.) 41.139

b.)10.067

c.)31.072

d.)0.000

 

Ans:  a

Level:  Moderate

Section:  5.5

 

 

 

  1. A model estimated using a dataset with 125 observations generates the following results.
Variable   b   Std. Error   t   P>|t|
x2 -0.01264 0.005519 -2.28937 0.022
x3 0.595792 0.014482 41.13934 0.000
x4 1.124589 0.877192 1.282032 0.200
x5 0.323742 0.060709 5.332661 0.000
Constant 8.86016 1.766116 5.016749 0.000
 

If you want to test the hypothesis b5 = .47.  What p-value does this test statistic generate if you are performing a two-tailed test?

a.)  0.000

b.)  ≃0.02

c.)  ≃0.01

d.)  0.05

 

Ans:  b

Level:  Moderate/Difficult

Section:  5.5

 

 

 

15.)  A model estimated using a dataset with 125 observations generates the following results.

Variable   b   Std. Error   t   P>|t|
x2 -0.01264 0.005519 -2.28937 0.022
x3 0.595792 0.014482 41.13934 0.000
x4 1.124589 0.877192 1.282032 0.200
x5 0.323742 0.060709 5.332661 0.000
Constant 8.86016 1.766116 5.016749 0.000
 

What test statistic would you use to test the hypothesis b5≥.25?

a.)  1.2147

b.)  5.3327

c.)  1.2948

d.) 0.0607

 

Ans:  a

Level:  Moderate

Section:  5.5

 

 

 

16.)  How can you estimate non-linear function forms using least squares?

a.)  estimate the linear approximation over small ranges at a time

b.)  transform, such as squaring or cubing, some explanatory variables.

c.)  use a very large sample so you do not have to assume the error terms are normally distributed

d.)  It cannot be done.  You need to use another estimation technique.

 

Ans:  b

Level:  Easy

Section:  5.6

 

 

 

17.)  If you have the following economic model

y = b1 + b2x – b3x2

What is dy/dx?

a.)  b2

b.)  b3+b2

c.)  b2 – 2b3x

d.)  b1 + 2b2

 

Ans:  c

Level:  Moderate

Section:  5.6

 

 

 

  1. You have the following economic model

                                    y = b1 + b2x + b3x2

If b2 is positive and b3 is negative what is the general shape of F(x)?

a.)  U-shape

b.)  Inverted U

c.)  Sigmoid

d.)  rectangular hyperbola

 

Ans:  b

Level:  Moderate

Section:  5.6

 

 

 

  1. What is an interaction term?

a.)  an additional variable that is the product of 2 other explanatory variables

b.)  a variable indicating 2 observations are related

c.)  a variable indicating an observation may be in the dataset multiple times

d.)  the expected value formed by multiplying a variable by its estimated coefficient.

 

Ans:  a

Level:  Easy

Section:  5.7

 

 

 

19.)  A model estimated using a dataset with 125 observations generates the following results.

 

SS df MS
Regression 919587.543 4 229896.9
Error 2590390.62 121 534.2113
Variable   b   Std. Error   t   P>|t|
x2 -0.0126355 0.005519 -2.28937 0.022
x3 0.5957923 0.014482 41.13934 0.000
x4 1.124589 0.877192 1.282032 0.200
x5 0.3237421 0.060709 5.332661 0.000
constant 8.86016 1.766116 5.016749 0.000

What is the R2 for this sample?

a.)  .2620

b.)  .3550

c.)  .0888

d.)  .2172

 

Ans:  a

Level:  Moderate

Section:  5.8

 

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