Deck 6: The Multiple Regression Model

Question 1

)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

Answer 1

D

Question 2

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.

Answer 2

A

Question 3

)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

Answer 3

A

Question 4

)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?

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

Question 5

)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?

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

Question 6

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

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

Question 7

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

A)The values of each x_ik are not random and are not exact linear functions of the other explanatory variables.
B)var(y_i. )= var(e_i)= $\sigma$ ²
C)The least squares estimators are BLUE.
D)cov(y_i,y_j)= cov(e_i,e_j)= 0; (i≠j)

Question 8

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

A)
B)
C)
D)

Question 9

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

A)so we will know how the estimate is distributed if H_o 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 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?

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

Question 11

)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, $\sigma$ ²
B)larger correlation between x₂ and x₃
C)smaller values of Ʃ(x_i2 - x̅₂)²
D)larger correlation between x₂ and y

Question 12

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)?

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

Question 13

)How should $\beta$ _k 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 x_k when all remaining variables are unchanged
B)the magnitude by which x_k varies in the model
C)the amount of variation in y explained by x_k in the model
D)the number of variables used in the model.

Question 14

)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?

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

Question 15

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?

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

Question 16

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?

A)0.000
B)≃0.02
C)≃0.01
D)0.05

Question 17

)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.

Question 18

)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?

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

Question 19

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.

Question 20

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

A) $\beta$ ₂
B) $\beta$ ₃+ $\beta$ ₂
C) $\beta$ ₂ - 2 $\beta$ ₃x
D) $\beta$ ₁ + 2 $\beta$ ₂