Questions 1-3 are based on the following information: Consider the following pop
ID: 1104248 • Letter: Q
Question
Questions 1-3 are based on the following information:
Consider the following population model for household spending on food:
food = + 1 inc + 2 hhsize + u , where food is food expenditure in dollars, inc is income, educ is the education level of household head, hhsize is the size of a household.
1. Suppose a researcher estimates this model, one can
a) be certain that R^2 will increase if adding household head’s age as an additional regressor.
b) be certain on the unit of measurement of regressors.
c.) be certain that R^2 may decrease if adding household head’s age as an additional regressor
d.) be certain that R^2 depends on the unit of measurement of the dependent variable.
2. Suppose that the variable for food expenditure is measured with errors, so food = food_c + e, where food is the mismeaured variable, while food_c is the true food expenditure, e is the measurement error which is independent of food_c. We would expect that
a) OLS estimates for the coefficients will all be biased
b) OLS estimates for the coefficients will all be unbiased
c) R^2 will increase compared with the case when food expenditure is not mismeasured
d.) both b) and c).
3. Suppose the data were collected through a telephone survey, and the last 4 digits of the households’ telephone number was accidentally included in the regression. Denote the coefficients as B3. We would expect
a.) the OLS estimates beta hat 1, beta hat 2, and beta hat 3 are all biased
b.) R squared will be smaller
c.) The OLS estimates beta hat 1, beta hat 2, beta hat 3 are unbiased
d.) Adjusted R squared will get larger
Explanation / Answer
1 (a) As one adds more regressors R^2 will increase R^2 is non decreasing in the number of regressors. So it is certain that R^2 will increase if adding household head’s age as an additional regressor.
2 (b) Inspite of the measurement error in the dependent variable, the OLS estimates still remain unbiased.
3 (c) When we overfit a model by including an unnecessary variable, then the OLS coefficients still remain unbiased.
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