Assignment #6 Multiple Regression Estimation

**Reading: ** Wooldridge Ch 3

**1. **A researcher uses data wages of working men to estimate the following equation:

where *educ *is years of schooling, *sibs *is number of siblings, *meduc *is mother’s years of schooling, and *feduc *is father’s years of schooling.

(i) Does *sibs *have the expected effect? Explain. Holding *meduc *and *feduc *fixed, by how much does *sibs *have to increase to reduce predicted years of education by one year?

(A noninteger answer is acceptable here.)

(ii) Discuss the interpretation of the coefficient on *meduc*.

(iii) Suppose that Man A has no siblings, and his mother and father each have 12 years of education. Man B has no siblings, and his mother and father each have 16 years of education. What is the predicted difference in years of education between B and A?

**2. **In a study relating college grade point average to time spent in various activities, you distribute a survey to several students. The students are asked how many hours they spend each week in four activities: studying, sleeping, working, and leisure. Any activity is put into one of the four categories, so that for each student, the sum of hours in the four activities must be 168.

(i) In the model

does it make sense to hold *sleep*, *work*, and *leisure *fixed, while changing *study*?

(ii) Explain why this model violates Assumption MLR.3.

(iii) How could you reformulate the model so that its parameters have a useful interpretation and it satisfies Assumption MLR.3?

**3. **Which of the following can cause OLS estimators to be biased?

(i) Heteroskedasticity.

(ii) Omitting an important variable.

(iii) A sample correlation coefficient

**4.** Suppose that average worker productivity at manufacturing firms (*avgprod *) depends on

two factors, average hours of training (*avgtrain*) and average worker ability (*avgabil *):

Assume that this equation satisfies the Gauss-Markov assumptions. If grants have been given to firms whose workers have less than average ability, so that *avgtrain *and *avgabil* are negatively correlated, what direction is the likely bias in β_{1 }obtained from the simple regression of *avgprod *on *avgtrain*? Will the regression under- or overestimate the effect of the program?

**5**. This is a computer exercise that can be completed in Excel or Gretl.

Use the data in HPRICE1 to estimate the model

where *price *is the house price measured in thousands of dollars.

(i) Write out the results in equation form.

(ii) What is the estimated increase in price for a house with one more bedroom, holding square footage constant?

(iii) What is the estimated increase in price for a house with an additional bedroom that is 140 square feet in size? Compare this to your answer in part (ii).

(iv) What percentage of the variation in price is explained by square footage and number of bedrooms?

(v) The first house in the sample has *sqrft= *2,438 and *bdrms *= 4. Find the predicted selling price for this house from the OLS regression line.

(vi) The actual selling price of the first house in the sample was $300,000 (so *price *=300). Find the residual for this house. Does it suggest that the buyer underpaid or overpaid for the house?

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