29. The Director of the Appalachian Commission is concerned with housing quality in the Appalachian counties within Kentucky and Tennessee. Policy analysts with the Commission have recommended that one mechanism to increase housing quality is to increase the Commission's per capita education expenditures in the county. Using a data set from a recent year that contains information for the counties within the Commission's jurisdiction, the analysts obtained the following bivariate regression results from R. HOUSQUAL is measured as the percentage of housing units in the county lacking some plumbing, so a lower percentage indicates higher quality housing. EDUCPCAP is measured as the per capita education expenditures in dollars per county. Im(formula = HOUSQUAL ~ EDUCPCAP, data = apl) Residuals: Min 1Q Median 3Q Max -18.5224 -4.8560 -0.9645 6.6128 12.9738 Coefficients: Estimate Std. Error t value Pr(> It!) (Intercept) 33.64068 2.51627 13.369 0.000000000000112 * * * EDUCPCAP 0.01239 0.00253 4.896 0.000036843976745 * ** Signif. codes: 0 * * 0.001 0.01 ' 0.05 / 0.1"1 Residual standard error: 8.319 on 28 degrees of freedom Multiple R-squared: 0.4612, Adjusted R-squared: 0.442 F-statistic: 23.97 on 1 and 28 DF, p-value: 0.00003684 > cv(mod1) 0.1798226 a. Write out the sample regression function. b. Interpret the values of the regression coefficient estimates c. Interpret the t and F statistics and their p-values d. Interpret the R-squared value e. Interpret the residual standard error and the coefficient of variation f. What should the analysts tell the Director about the use of education in enhancing housing quality