Ch4 Test Bank Prediction Goodness-Of-Fit And Modeling Issues

File: Ch04, Chapter 4, Prediction, Goodness-of-Fit, and Modeling Issues

Multiple Choice

1. Which of the following leads to large forecast errors?

a. Larger sample size, N.

b. Variation in the explanatory variable, x, is large.

c. Overall uncertainty in the model, as measured by ², is smaller.

d. The value of (x₀ – x̄) ² is larger.

2. At what values of x₀ will the standard error of the forecast be smallest?

a. x₀ = 0

b. x₀ =x̅

c. x₀² = ̂²

d. x₀ = t_c se(f)

3. Which of the following expressions is NOT equal to Ʃ(y_i - y̅)² ?

a. Ʃ(ŷ_i-y̅)²+ Ʃe_i²

b. SSR + SSE

c. SSR/SSE

d. SST

4. What does R2, the coefficient of determination, measure?

a. The probability of the true value falling within the forecast interval

b. The p-value on the coefficient we are using to test our hypothesis of interest

c. The confidence interval of the error terms as determined by the coefficients

d. The proportion of the variation in y explained by x within the regression model

5. Which of the following expressions describes the relationship between the coefficient of determination, R², and the sample correlation coefficient, r_XY?

a.

b.

c.

d.

6. You have estimated a regression model and your printout includes the following information:

s_xy= 3614.00

s_x = 12.72

s_y = 394.61

SST = 758912.00

What is R² for this regression model?

a. 0.72

b. 0.11

c. 0.03

d. 0.53

7. You have estimated a regression model and your printout includes the following information:

s_xy= 3614.00

s_x = 12.72

s_y = 394.61

SST = 758912.00

Use this information to calculate SSE.

a. 546,416.64

b. 212,495.36

c. 381.89

d. 5019.44

8. Which of the following will change if you scale the dependent variable in a simple regression model?

a. p-value

b. t-value of ₂

c. R²

d. ₁

9. When should a researcher consider transforming the explanatory variable in a simple linear regression model?

a. When a data plot suggests there is a non-linear functional form

b. To get a coefficient estimate with the sign predicted by economic theory

c. To reduce the variation in the explanatory variable

d. To maximize SSR

10. When should a researcher consider transforming the explanatory variable in the simple linear regression model?

a.) To estimate a coefficient on the dependent variable that matches economic theory

b.) To allow non-constant marginal effects

c.) To reduce variance in the dependent variable

d.) To reduce

11. How do you interpret the estimated value of ₂ in the following model?

ln(y) = ₁ + ₂ * ln(x)

a. The slope of the line representing the relationship between y and x

b. The elasticity of y with respect to x

c. Cannot be determined without more information

d. The mean value of ln(y) when ln(x) = 0

12. Suppose you estimate a linear regression model with a linear-log form, . In this case, a one percent change in the dependent variable would lead to a _____ change in y.

a. unit

b. unit

c. percent

d. percent

13. You have estimated the following simple regression model: y = 379 + 1.44 x³

What does this model predict y to be when x = 8.49?

a. 415.68

b. 690.39

c. 1260.22

d. 2205.47

14. You have estimated the following simple regression model: y = 379 + 1.44 x³

What is the elasticity when x = 8.49?

a. 263.19

b. 311.39

c. 2.10

d. -24.7

15. You have estimated a model of two variables related such that: ln(y) = 17.3 - .04 x

If x decreases by 2 units, what is the expected change in y?

a. y decreases by .08 units.

b. y increases by 8 percent.

c. y increases by 4 units.

d. y decreases by 8 percent.

16. While working with the sales manager of your firm you have estimated the following model of sales volume as a function of monthly household income:

(0.781) (0.392)

Where Q is monthly sales volume, I is monthly household income in thousands, and standard errors are listed below the parameter estimates. What is the income elasticity of your firm’s product?

a. 1.212

b. 2.206

c. 3.418

d. 4.630

17. While working with the sales manager of your firm you have estimated the following model of sales volume as a function of monthly household income:

(0.781) (0.392)

Where Q is monthly sales volume, I is monthly household income in thousands, and standard errors are listed below the parameter estimates. What does the model predict sales volume to be if using the corrected predictor when income is $4000 per month?

a. 708,133.68

b. 723,146.11

c. 163.73

d. 167.20

18. When the residuals from a simple regression model appear to be correlated with x, this is known as _____.

19. If a scatter plot of the data reveals an inverted U shape, what data transformation would allow it to be estimated with simple linear regression?

20. A measure of the symmetry of a distribution is _____.

21. What is the skewness of the normal distribution?

22. What about the distribution of a random variable does kurtosis measure?

23. What is the kurtosis measure of the normal distribution?