Use the data in MEAP93 to answer this question.

(i) Estimate the model math10 5 b0 1 b1log1expend2 1 b2lnchprg 1 u, and report the results in the usual form, including the sample size and R-squared. Are the signs of the slope coefficients what you expected? Explain.

(ii) What do you make of the intercept you estimated in part (i)? In particular, does it make sense to set the two explanatory variables to zero? [Hint: Recall that log112 5 0.]

(iii) Now run the simple regression of math10 on log(expend), and compare the slope coefficient with the estimate obtained in part (i). Is the estimated spending effect now larger or smaller than in part (i)?

(iv) Find the correlation between lexpend 5 log1expend2 and lnchprg. Does its sign make sense to you?

(v) Use part (iv) to explain your findings in part (iii).

C8 Use the data in DISCRIM to answer this question. These are code–level data on prices for various items at fast-food restaurants, along with characteristics of the zip code population, in New Jersey and Pennsylvania. The idea is to see whether fast-food restaurants charge higher prices in areas with a larger concentration of blacks.

(i) Find the average values of prpblck and income in the sample, along with their standard deviations. What are the units of measurement of prpblck and income?

(ii) Consider a model to explain the price of soda, psoda, in terms of the proportion of the population that is black and median income:

psoda 5 b0 1 b1prpblck 1 b2income 1 u.

Estimate this model by OLS and report the results in equation form, including the sample size and R-squared. (Do not use scientific notation when reporting the estimates.) Interpret the coefficient on prpblck. Do you think it is economically large?

(iii) Compare the estimate from part (ii) with the simple regression estimate from psoda on prpblck.

Is the discrimination effect larger or smaller when you control for income?

(iv) A model with a constant price elasticity with respect to income may be more appropriate.

Report estimates of the model log1psoda2 5 b0 1 b1prpblck 1 b2log1income2 1 u.

If prpblck increases by .20 (20 percentage points), what is the estimated percentage change in psoda? (Hint: The answer is 2.xx, where you fill in the “xx.”)

(v) Now add the variable prppov to the regression in part (iv). What happens to b^

prpblck?

(vi) Find the correlation between log(income) and prppov. Is it roughly what you expected?

(vii) Evaluate the following statement: “Because log(income) and prppov are so highly correlated, they have no business being in the same regression.”

C9 Use the data in CHARITY to answer the following questions:

(i) Estimate the equation gift 5 b0 1 b1mailsyear 1 b2giftlast 1 b3propresp 1 u by OLS and report the results in the usual way, including the sample size and R-squared.

How does the R-squared compare with that from the simple regression that omits giftlast and propresp?