Question

6. The error term in linear regression models is assumed:

(A) having the mean of zero

(B) having the variance of zero

(C) being normally distributed with a positive mean

(D) being normally distributed with a negative mean

7.How should β 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.

8. What are the consequences of using least squares when heteroskedasticity is present?

(A) None of the above

(B) Confidence intervals and hypothesis testing are inaccurate due to inflated standard errors.

(C) All coefficient estimates are biased for variables correlated with the error term.

(D) No consequences, coefficient estimates are still unbiased.

9. The following equation has been used to estimate wages:

ln ⁡ ( Y ) = β 1 + β 2 E D U + β 3 E X P E R + β 4 E X P E R 2 + e

where Y is income, EDU is years of education and EXPER is experience in the field. If you suspect that males earn higher wages than females and that the wage difference increases with education, how would you adjust the econometric model to estimate wages?

(A) Include a binary variable for MALE and an interaction term equal to MALE*EDU

(B) Include a binary variable for gender, MALE.

(C) Include an interaction term equal to MALE*EDU.

(D) Include an indicator variable for MALE and one for FEMALE.

10. You have estimated the following equation using OLS:

y ^ = 33.75 + 1.45 M A L E

where y is annual income in thousands and MALE is an indicator variable such that it is 1 for males and 0 for females. According to this model, wha tis the average income for females?

(A) $33,750

(B) $35,200

(C) $32,300

(D) Cannot be determined.

Answer 1

Question 6) answer is (A) having mean 0

The error term accounts for the variation in the dependent variable that the independent variables do not explain. Random chance should determine the values of the error term. For a model to be unbiased, the average value of the error term must equal zero.

Question 7) answer is (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.

The interpretation of is the change (increase or decrease depending on the sign) in the average outcome ( ) when the explanatory variable increases by one unit

Question 8) answer is (B) Confidence intervals and hypothesis testing are inaccurate due to inflated standard errors.

While heteroscedasticity does not cause bias in the coefficient estimates, it does make them less precise. Lower precision increases the likelihood that the coefficient estimates are further from the correct population value.

Heteroscedasticity tends to produce p-values that are smaller than they should be. This effect occurs because heteroscedasticity increases the variance of the coefficient estimates but the OLS procedure does not detect this increase.

Question 9) answer is (A)  Include a binary variable for MALE and an interaction term equal to MALE*EDU

In complex study areas, the independent variables might interact with each other. Interaction effects indicate that a third variable influences the relationship between an independent and dependent variable. This type of effect makes the model more complex, but if the real world behaves this way, it is critical to incorporate it in the model.

To understand potential interaction effects, compare the lines from the interaction plot. An interaction plot is a line graph that reveals the presence or absence of interactions among independent variables.

If the lines are parallel, there is no interaction. & If the lines are not parallel, there is an interaction.  

Question 10) answer is (A) $ 33,750