[This exercise requires the material in Appendix A13.1.] Suppose that the regression model Ya+B+B+6 is estimated by least squares. Show that the residuals, e., from the fitted model sum to 11.

47. A study was conducted to assess the influence of various factors on the start of new firms in the electronics components industry in urban areas. For a sample of seventy standard metropolitan statistical areas, the following model was estimated: y=-59.31 +4.983x, +2.198x +3.816-310x where (1.156) (210) (2.063) (330) -886x, +3.215x + .085x R = .766 (3.055) (1.568) (.354) y=New business starts in the industry XPopulation, in millions X Industry size x = Measure of economic quality of life x. Measure of political quality of life XMeasure of environmental quality of life Xe Measure of health and educational quality of life x = Measure of social quality of life The figures in parentheses beneath the coefficient estimates are their estimated standard errors.

(a) Interpret the estimated partial regression coefficients.

(b) Interpret the coefficient of determination.

(c) Find a 90% confidence interval for the increase in new business starts resulting from a 1-unit increase in the economic quality of life, with all other variables unchanged.

(d) Test against a two-sided alterative at the 5% significance level the null hypothesis that, all else remaining equal, the environmental quality of life does not influence new business starts.

(e) Test against a two-sided alternative at the 5% significance level the null hypothesis that, all else remaining equal, the health and educational quality of life does not influ- ence new business starts.

(f) Test the null hypothesis that taken together, these seven independent variables do not influence new business starts.