5e Full Test Bank Ch.5 The Multiple Regression Model

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

2. How should _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

3. Given the general multiple regression model and letting , the assumption that is called the _____ assumption and the assumption that is called the _____ assumption.

a. conditional homoscedasticity; strict exogeneity

b. conditionally uncorrelated errors; strict exogeneity

c. strict exogeneity; conditional homoscedasticity

d. strict exogeneity; conditionally uncorrelated errors

4. What is the unbiased estimator of ² in the multiple regression model?

a.

b.

c.

d.

5. Why does the denominator of ̂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

6. In the multiple regression model, which of the following will lead to larger variances of the least squares estimates?

a. Smaller error variances

b. Smaller sample size

c. Less variation in an explanatory variable around its mean

d. Smaller correlation between explanatory variables

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

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

9. 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

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

What are the endpoints for the 95% confidence interval for ₃?

a. (-0.6842, 1.8758)

b. (-1.3842, 2.5758)

c. (.5672, 6245)

d. (-40.5435, 41.7251)

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

What are the endpoints for the 99% confidence interval for ₅?

a. (0.1623, 0.4852)

b. (-5.0089, 5.6564)

c. (0.2630, 0.3845)

d. (0.1786, 0.4688)

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

If you want to test the hypothesis that ₃ =0.45, what is the test statistic from this sample?

a. 41.139

b. 10.067

c. 31.072

d. 0.000

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

If you want to test the hypothesis 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

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

What test statistic would you use to test the hypothesis ₅≥.25?

a. 1.2147

b. 5.3327

c. 1.2948

d. 0.0607

15. 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.

16. Assume you have the following economic model: y = ₁ + ₂x - ₃x²

What is dy/dx?

a. ₂

b. ₃+₂

c. ₂ – 2₃x

d. ₁ + 2₂

17. You have the following economic model: y = ₁ + ₂x + ₃x²

If ₂ is positive and ₃ is negative what is the general shape of F(x)?

a. U-shape

b. Inverted U

c. Sigmoid

d. Rectangular hyperbola

18. When dealing with time series data, the multiple regression assumption of _____ has a strong likelihood of being violated. It is possible to show that estimates are _____.

a. strict exogeneity; unbiased

b. conditional homoscedasticity; unbiased

c. conditional homoscedasticity; consistent

d. strict exogeneity; consistent

19. Briefly describe the five required assumptions of the multiple regression model.

2. Strict exogeneity – The conditional expectations of the random error given all explanatory variable observations is zero, or where .

3. Conditional homoscedasticity – the variance of the error term conditional on all of the explanatory variables is a constant, or .

4. Conditional uncorrelated errors – The covariance between different error terms, conditional on all of the explanatory variables, is zero, or for .

5. No exact linear relationship exists between the explanatory variables – it is not possible to express one of the explanatory variables as an exact linear function of the other explanatory variables. Mathematically: the only values of that satisfy

Level: Easy – Knowledge

AACBS: Reflective Thinking

Section 5.1

20. Briefly describe the two conditions that are sufficient to establish that an estimator is consistent.

2. The variance of the estimator converges to zero as the sample size increases -

Level: Easy – Knowledge

AACSB: Reflective Thinking

Section: 5.7