Carol is investigating the impact of brand expenditures on firms' sales. She is also interested in if this varies in domestically owned firms (D) versus foreign owned firms (F). She gathers information on sales (S) and expenditures on brand development (B) for a sample of 200 clothing retailing firms, 140 of whom are domestic owned (D) and 60 of whom are foreign owned (F). She runs a regression of the form: 1]\":(5311. ) :(r + f)'1l"l(A/.)i ) + z-'t. The results of her regression analysis are given in the Table below. Regression results: Dependent variable is 111(3) Whole sample D firms F firms intercept 0.35 0.21 0.48 (2.35) (2.16) (3.15) In (B) 0.21 0. 18 0.29 (2.24) (1.79) (3.13) R 0.280 0. 115 0.315 N 200 140 60 t-ratios are in parenthesesII. Outline how a researcher tests for significance of regression coefficients. (7 marks) Answers should go through the steps of setting up the hypothesis (8:0), the set up of the t-test and the need to compare with the critical t- values. Good answers included correct degrees of freedom, significance levels, type 1 errors. III. What can Carol conclude about the significance of the coefficients in the above regressions, the magnitude of the impact of advertising on sales and the magnitude of the R2? (15 marks) As the variables are in logs the answers should interpret coefficient values in terms of % changes. They should have noted that AD is significant in the whole sample and for the F firms but not the D firms. They should have explained the R2 Could also have indicated that df differ between D and F. Answers were generally good on explaining the R2, and significance of coefficients, less so on interpreting coefficients and comparing these across D and F firms and with the whole sample. IV. What are standard errors of coefficients? What are they affected by? Finally, what is the relationship between standard errors and t- ratios? (7 marks) Discussion of standard errors of coefficients, including formula, noting variables which increase/decrease standard errors. Show formula linking t values to standard errors, and thus the importance of the standard errors in yielding coefficients of statistical significance