Using (N=2005) observations, we examine the relationship between food expenditures away from home per person in the

Question:

Using $N=2005$ observations, we examine the relationship between food expenditures away from home per person in the past month as a function of household monthly income, the highest level of education of a household member, and region of the country. The full equation of interest is

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where $C O L L E G E=1$ if the highest education of a household member is a college degree, $A D V A N C E D=1$ if the highest education of a household member is an advanced degree (such as a Master's or Ph.D.). The regional indicators equal one if the household lives in that region and are zero otherwise.

a. The estimated value of $\beta_{2}$ is 0.427 with a standard error of 0.035. Construct and interpret a $95 \%$ interval estimate.

b. The estimated value of $\delta_{2}$ is 0.270 with a standard error of 0.0544 . Construct and interpret a $95 \%$ interval estimate using the rough calculation in Section 7.3.1.

c. Use the exact calculation discussed in Section 7.3.1 to estimate the predicted effect on food expenditure per person away from home for a household having a member with an advanced degree.

d. What is the null hypothesis, in terms of the model parameters, that the highest level of education achieved by a household member does not matter? What is the test statistic for this hypothesis? What is the $5 \%$ rejection region? The sum of squared residuals from the full model is 1586 and $S S E$ from the model omitting the education variables is 1609 . Can we conclude that the education variables are important predictors of food expenditures away from home?

e. In the full model, the reported $t$-value for $C O L L E G E$ is 0.34. What can we conclude from that?

f. The estimated value of $\theta_{2}$ is 0.088. What is the estimated expected value of $\ln (F O O D A W A Y)$ for a household with $\$ 10,000$ per month income, with a member with an advanced degree, and who live in the south? Calculate the natural and corrected predictors of expenditure on food away from home per member for this household.

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