The data file malawi_small contains survey data from Malawi during 2007-2008 on total household expenditures in the prior month (in Malawian Kwacha) as well as expenditures on categories of goods such as food, clothes, and fuel.

a. Define the proportion of expenditure on food consumed away from home as PFOODAWAY= FOODAWAY/TOTEXP. Construct a histogram for PFOODAWAY and its summary statistics. What percentage of the sample has a zero value for PFOODAWAY. What does that imply about their expenditures last month?

b. Create the variable FOODAWAY \(=\) PFOODAWAY \(\times\) TOTEXP . Construct a histogram for FOOD\(A W A Y\) and another histogram for FOODAWAY if FOODAWAY \(>0\). Compare the summary statistics for TOTEXP for households with FOODAWAY \(>0\) to those with FOODAWAY \(=0\). What differences do you observe?

c. Estimate the linear regression model FOODAWAY \(=\beta_{1}+\beta_{2}\) TOTEXP \(+e\) twice, once for the full sample, and once using only households for whom FOODAWAY \(>0\). What differences in slope estimates do you observe? How would you explain these differences to an audience of noneconomists?

d. Calculate the fitted values from each of the estimated models in part

(c) and plot the fitted values, and FOODAWAY values, versus TOTEXP. Think about how the least squares estimation procedure works to fit a line to data. Explain the relative difference in the two estimations based on this intuition.