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. Estimate the linear regression FOODAWAY \(=\beta_{1}+\beta_{2} I N C O M E+e\). Interpret the estimated slope.

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

c. Estimate the linear regression FOODAWAY \(=\alpha_{1}+\alpha_{2} A D V A N C E D+e\). Interpret the estimated coefficient of ADVANCED.

d. What are the sample means of FOODAWAY for households including a member with an advanced degree? With no advanced degree member? How do these values relate to the regression in part (c)?