Question 1

)How should $\beta$k in the general multiple regression model be interpreted?

Accepted Answer

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.  A

Question 2

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

Accepted Answer

A)  larger error variances, σ\sigmaσ 2
B)  larger correlation between x2 and x3
C)  smaller values of Ʃ(xi2 - x̅2) 2
D)  larger correlation between x2 and y  D

Question 3

)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?

Accepted Answer

A)  2.426
B)  2.708
C)  2.423
D)  2.704 A

Question 4

)A model estimated using a dataset with 65 observations generates the following results.  What are the endpoints for the 99% confidence interval for $\beta$5?

Accepted Answer

A)  (0.1623,0.4852) 
B)  (-5.0089 ,5.6564) 
C)  (0.2630 ,0.3845) 
D)  (0.1786 ,0.4688)

Question 5

)Why does the denominator of$\sigma$2 need to be the same as the degrees of freedom in the model?

Accepted Answer

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

Question 6

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 ______________.

Accepted Answer

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.

Question 7

)A model estimated using a dataset with 125 observations generates the following results.  What is the R2 for this sample?

Accepted Answer

A)  .2620
B)  .3550
C)  .0888
D)  .2172

Question 8

)A model estimated using a dataset with 65 observations generates the following results.  If you want to test the hypothesis that $\beta$3 =0.45,what is the test statistic from this sample?

Accepted Answer

A)  41.139
B)  10.067
C)  31.072
D)  0.000

Question 9

A model estimated using a dataset with 125 observations generates the following results.  What are the endpoints for the 95% confidence interval for $\beta$3?

Accepted Answer

A)  (-0.6842,1.8758) 
B)  (-1.3842,2.5758) 
C)  (.5672,6245) 
D)  (-40.5435 ,41.7251)

Question 10

)The matrix below represents the variance-covariance matrix estimated from the multiple regression model:  Which 2 elements of the matrix should always be equal?

Accepted Answer

A)  A & I
B)  B & H
C)  C & G
D)  D & F

Question 11

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

Accepted Answer

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) =  σ\sigmaσ 2
C)  The least squares estimators are BLUE.
D)  cov(yi,yj) = cov(ei,ej) = 0; (i≠j)

Question 12

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

Accepted Answer

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.

Question 13

)A model estimated using a dataset with 125 observations generates the following results.  What test statistic would you use to test the hypothesis $\beta$5≥.25?

Accepted Answer

A)  1.2147
B)  5.3327
C)  1.2948
D)  0.0607

Question 14

)The matrix below represents the variance-covariance matrix estimated from the multiple regression model:  Which element of the matrix cannot be negative?

Accepted Answer

A)  A
B)  B
C)  C
D)  D

Question 15

)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?

Accepted Answer

A)  242
B)  120
C)  ∞
D)  241

Question 16

)If you have the following economic model y = $\beta$1 + $\beta$2x - $\beta$3x2
What is dy/dx?

Accepted Answer

A)   β\betaβ 2
B)   β\betaβ 3+ β\betaβ 2
C)   β\betaβ 2 - 2 β\betaβ 3x
D)   β\betaβ 1 + 2 β\betaβ 2

Question 17

)What is the unbiased estimator of $\sigma$2 in the multiple regression model?

Accepted Answer

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Question 18

You have the following economic model y = $\beta$1 + $\beta$2x + $\beta$3x2
If $\beta$2 is positive and $\beta$3 is negative what is the general shape of F(x)?

Accepted Answer

A)  U-shape
B)  Inverted U
C)  Sigmoid
D)  rectangular hyperbola

Question 19

What is an interaction term?

Accepted Answer

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.

Question 20

A model estimated using a dataset with 125 observations generates the following results.  If you want to test the hypothesis $\beta$5 = .47.What p-value does this test statistic generate if you are performing a two-tailed test?

Accepted Answer

A)  0.000
B)  ≃0.02
C)  ≃0.01
D)  0.05

Exam 6: The Multiple Regression Model

) How should $\beta$ _k in the general multiple regression model be interpreted?

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

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

) Why does the denominator of $\sigma$ ₂ need to be the same as the degrees of freedom in the model?

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 model estimated using a dataset with 125 observations generates the following results. What is the R² for this sample?

) The matrix below represents the variance-covariance matrix estimated from the multiple regression model: Which 2 elements of the matrix should always be equal?

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

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

) The matrix below represents the variance-covariance matrix estimated from the multiple regression model: Which element of the matrix cannot be negative?

) 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?

) If you have the following economic model y = $\beta$ ₁ + $\beta$ ₂x - $\beta$ ₃x² What is dy/dx?

) What is the unbiased estimator of $\sigma$ ² in the multiple regression model?

You have the following economic model y = $\beta$ ₁ + $\beta$ ₂x + $\beta$ ₃x² If $\beta$ ₂ is positive and $\beta$ ₃ is negative what is the general shape of F(x) ?

What is an interaction term?

Exam 6: The Multiple Regression Model

) How should β\betaβ k in the general multiple regression model be interpreted?

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

) 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 model estimated using a dataset with 65 observations generates the following results. What are the endpoints for the 99% confidence interval for β\betaβ 5?

) Why does the denominator of σ\sigmaσ 2 need to be the same as the degrees of freedom in the model?

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 model estimated using a dataset with 125 observations generates the following results. What is the R2 for this sample?

) A model estimated using a dataset with 65 observations generates the following results. If you want to test the hypothesis that β\betaβ 3 =0.45,what is the test statistic from this sample?

A model estimated using a dataset with 125 observations generates the following results. What are the endpoints for the 95% confidence interval for β\betaβ 3?

) The matrix below represents the variance-covariance matrix estimated from the multiple regression model: Which 2 elements of the matrix should always be equal?

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

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

) A model estimated using a dataset with 125 observations generates the following results. What test statistic would you use to test the hypothesis β\betaβ 5≥.25?

) The matrix below represents the variance-covariance matrix estimated from the multiple regression model: Which element of the matrix cannot be negative?

) 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?

) If you have the following economic model y = β\betaβ 1 + β\betaβ 2x - β\betaβ 3x2 What is dy/dx?

) What is the unbiased estimator of σ\sigmaσ 2 in the multiple regression model?

You have the following economic model y = β\betaβ 1 + β\betaβ 2x + β\betaβ 3x2 If β\betaβ 2 is positive and β\betaβ 3 is negative what is the general shape of F(x) ?

What is an interaction term?

A model estimated using a dataset with 125 observations generates the following results. If you want to test the hypothesis β\betaβ 5 = .47.What p-value does this test statistic generate if you are performing a two-tailed test?

) How should $\beta$ _k in the general multiple regression model be interpreted?

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

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

) Why does the denominator of $\sigma$ ₂ need to be the same as the degrees of freedom in the model?

) A model estimated using a dataset with 125 observations generates the following results. What is the R² for this sample?

) If you have the following economic model y = $\beta$ ₁ + $\beta$ ₂x - $\beta$ ₃x² What is dy/dx?

) What is the unbiased estimator of $\sigma$ ² in the multiple regression model?

You have the following economic model y = $\beta$ ₁ + $\beta$ ₂x + $\beta$ ₃x² If $\beta$ ₂ is positive and $\beta$ ₃ is negative what is the general shape of F(x) ?