Problem 3 addressed the cross-sectional variation in the number of financial analysts who follow a company. in that problem, company size and debt-to-equity ratios were the in- dependent variables. you receive a suggestion that membership in the S&P 500 index should be added to the model as a third independent variable; the hypothesis is that

Problem 3 addressed the cross-sectional variation in the number of financial analysts who follow a company. in that problem, company size and debt-to-equity ratios were the in- dependent variables. you receive a suggestion that membership in the S&P 500 index should be added to the model as a third independent variable; the hypothesis is that there is greater demand for analyst coverage for stocks included in the S&P 500 because of the widespread use of the S&P 500 as a benchmark. a. write a multiple regression equation to test whether analyst following is systematically higher for companies included in the S&P 500 index. also include company size and debt-to-equity ratio in this equation. use the notations below. (analyst following)i = natural log of (1 + number of analysts following company i) Sizei = natural log of the market capitalization of company i in millions of dollars (d/e)i = debt-to-equity ratio for company i S&Pi = inclusion of company i in the S&P 500 index (1 if included, 0 if not included) in the above specification for analyst following, 1 is added to the number of analysts following a company because some companies are not followed by any analyst, and the natural log of 0 is indeterminate. B. State the appropriate null hypothesis and alternative hypothesis in a two-sided test of significance of the dummy variable. C. The following table gives estimates of the coefficients of the above regression model for a randomly selected sample of 500 companies. The data are for the year 2002. determine whether you can reject the null hypothesis at the 0.05 significance level (in a two-sided test of significance). Coefficient estimates from regressing analyst Following on Size, debt-to-equity ratio, and S&P 500 Membership, 2002 intercept Sizei (d/e)i S&Pi n = 500 Coefficient −0.0075 0.2648 −0.1829 0.4218 Standard error 0.1218 0.0191 0.0608 0.0919 t-Statistic −0.0616 13.8639 −3.0082 4.5898 Source: First Call/Thomson Financial, Compustat. d. Consider a company with a debt-to-equity ratio of 2/3 and a market capitalization of $10 billion. according to the estimated regression equation, how many analysts