Consumer expenditure data from 2013 are contained in the file cex5_small. [Note: cex5 is a larger version with more observations and variables.] Data are on three-person households consisting of a husband and wife, plus one other member, with incomes between \(\$ 1000\) per month to \(\$ 20,000\) per month. FOODAWAY is past quarter's food away from home expenditure per month per person, in dollars, and INCOME is household monthly income during past year, in \(\$ 100\) units.

a. Construct a histogram of FOODAWAY and its summary statistics. What are the mean and median values? What are the 25 th and 75 th percentiles?

b. What are the mean and median values of FOODAWAY for households including a member with an advanced degree? With a college degree member? With no advanced or college degree member?

c. Construct a histogram of \(\ln (\) FOODAWAY) and its summary statistics. Explain why FOODAWAY and \(\ln\) (FOODAWAY) have different numbers of observations.

d. Estimate the linear regression \(\ln (F O O D A W A Y)=\beta_{1}+\beta_{2} I N C O M E+e\). Interpret the estimated slope.

e. Plot \(\ln (F O O D A W A Y)\) against INCOME, and include the fitted line from part (d).

f. Calculate the least squares residuals from the estimation in part (d). Plot them vs. INCOME. Do you find any unusual patterns, or do they seem completely random?