The data set 401 $\mathrm{KSUBS}$ contains information on net financial wealth (nettfa), age of the survey respondent $(a g e),$ annual family income (inc), family size (fsize), and participation in certain pension plans for people in the United States. The wealth and income variables are both recorded in thousands of dollars. For this question, use only the data for single-person households (so fsize$=1 )$ .

(i) How many single-person households are there in the data set?

(ii) Use OLS to estimate the model

nettfa$=\beta_{0}+\beta_{1} i n c+\beta_{2} a g e+u$

and report the results using the usual format. Be sure to use only the single-person households in the sample. Interpret the slope coefficients. Are there any surprises in the slope estimates?

(iii) Does the intercept from the regression in part (ii) have an interesting meaning? Explain.

(iv) Find the $p$ -value for the test $\mathrm{H}_{0} : \beta_{2}=1$ against $\mathrm{H}_{1} : \beta_{2}<1 .$ Do you reject $\mathrm{H}_{0}$ at the 1$\%$ significance level?

(v) If you do a simple regression of netfa on inc, is the estimated coefficient on $i n c$ much different from the estimate in part (ii)? Why or why not?