The following information relates to Questions 37-45 Brad Varden, a junior analyst at an actively managed mutual fund, is responsible for research on a subset of the 500 large-cap equities the fund follows. Recently, the fund has been paying close attention to management turnover and to publicly available environmental, social, and governance (ESG) ratings. Varden is given the task of investigating whether any significant relationship exists between a company's profitability and either of these two characteristics . Colleen Quinni, a senior analyst at the fund, suggests that as an initial step in his report back to her. Statistic investigation, Varden should perform a multiple regression analysis on the variables and Chapter 8 Multiple Regression 447 Varden knows that Quinni is an expert at quantitative research, and she once told Varden that after you get an idea, you should formulate a hypothesis, test the hypothesis, and analyze the results, Varden expects to find that ESG rating is negatively related to ROE and CEO tenure is positively related to ROE. He considers a relationship meaningful when it is statistically significant at the 0.05 level. To begin, Varden collects values for ROE, CEO tenure, and ESG rating for a sample of 40 companies from the large-cap security universe. He performs a multiple regression with ROE (in percent) as the dependent variable and ESG rating and CEO tenure (in years) as the independent variables: Y,= b + b Xu + b2X2 + Exhibit 1 shows the regression results. EXHIBITI Regression Statistics Y = 9.442 + 0.069X+0.681X31 Coefficient Standard Error p-Value Intercept 9.442 3.343 (ESG variable) 0.069 0.058 bz (Tenure variable) 0.681 0.295 ANOVA DF SS MSS Significance F Regression 240.410 4.161 0.023 Residual 1069.000 Total 1309.410 Multiple R R Adjusted R Sandard error (%) Observations DF Associates is one of the companies Varden follows. He wants to predict its ROE using his regression model. DF Associates' corporate ESG rating is 55, and the company's CEO has been in that position for 10.5 years. Varden also wants to check on the relationship between these variables and the dividend growth rate (divgr), so he completes the correlation matrix shown in Exhibit 2. 0.008 2.824 1.201 2.308 0.238 0.027 F 2 120.205 28.892 37 39 0.428 0.183 0.139 5.375 40 EXHIBIT 2 Correlation Matrix ESG Tenure ROE Divgr ROE ESG Tenure Divgt 1.0 0.446 0.369 0.117 1.0 1.0 0.091 0.046 0.028 1.0 Quantitative Investment Analysis 448 Investigating further , Varden determines that dividend growth is not a linese combination of CEO tenure and Esg rating. He is unclear about how additional independent variables would affect the significance of the regression, so he asks Quinni, "Given this correlation matrix, will both R and adjusted R automatically increase if I add dividend growth as a third independent variable?" The discussion continues, and Quinni asks two questions. 1. What does your F-statistic of 4.161 tell you about the regression? 2. In interpreting the overall significance of your regression model , which statistic do you believe is most relevant: R', adjusted Re", or the F-statistic? Varden answers both questions correctly and says he wants to check two more ideas. He believes the following: 1. ROE is less correlated with the dividend growth rate in firms whose CEO has been in office more than 15 years, and 2. CEO tenure is a normally distributed random variable. Later, Varden includes the dividend growth rate as a third independent variable and runs the regression on the fund's entire group of 500 large-cap equities. He finds that the adjusted R is much higher than the results in Exhibit 1. He reports this to Quinni and says, "Adding the dividend growth rate gives a model with a higher adjusted R. The three-variable model is clearly better." Quinni cautions, I don't think you can conclude that yet." 37. Based on Exhibit 1 and given Varden's expectations, which is the best null hypothesis and conclusion regarding CEO tenure? A. 62 S 0; reject the null hypothesis B. by = 0; cannot reject the null hypothesis C. b2 2 0; reject the null hypothesis 38. At a significance level of 1%, which of the following is the best interpretation of the regression coefficients with regard to explaining ROE? A. ESG is significant, but tenure is not. B. Tenure is significant, but ESG is not. C. Neither ESG nor tenure is significant. 39. Based on Exhibit 1, which independent variables in Varden's model are significant at the 0.05 level? A. ESG only B. Tenure only C. Neither ESG nor tenure 40. Based on Exhibit 1, the predicted ROE for DF Associates is closest to: A. 10.957%. B. 16.593%. C. 20.388%. 41. Based on Exhibit 2, Quinni's best answer to Varden's question about the effect of adding a third independent variable is: A.no for R and no for adjusted R. B. yes for R and no for adjusted R. C. yes for R and yes for adjusted R. Chapter 8 Multiple Regression 449 42. Based on Exhibit 1, Varden's best answer to Quinni's question about the F-statistic is: A. both independent variables are significant at the 0.05 level. B. neither independent variable is significant at the 0.05 level. C. at least one independent variable is significant at the 0.05 level. 43. Varden's best answer to Quinni's question about overall significance is: A. R. B. adjusted R. C. the F-statistic. 44. If Varden's beliefs about ROE and CEO tenure are true, which of the following would violate the assumptions of multiple regression analysis? A. The assumption about CEO tenure distribution only B. The assumption about the ROE/dividend growth correlation only C. The assumptions about both the ROE/dividend growth correlation and CEO tenure distribution 45. The best rationale for Quinni's caution about the three-variable model is that the: A. dependent variable is defined differently. B. sample sizes are different in the two models. C. dividend growth rate is positively correlated with the other independent variables. The following information relates to Questions 37-45 Brad Varden, a junior analyst at an actively managed mutual fund, is responsible for research on a subset of the 500 large-cap equities the fund follows. Recently, the fund has been paying close attention to management turnover and to publicly available environmental, social, and governance (ESG) ratings. Varden is given the task of investigating whether any significant relationship exists between a company's profitability and either of these two characteristics . Colleen Quinni, a senior analyst at the fund, suggests that as an initial step in his report back to her. Statistic investigation, Varden should perform a multiple regression analysis on the variables and Chapter 8 Multiple Regression 447 Varden knows that Quinni is an expert at quantitative research, and she once told Varden that after you get an idea, you should formulate a hypothesis, test the hypothesis, and analyze the results, Varden expects to find that ESG rating is negatively related to ROE and CEO tenure is positively related to ROE. He considers a relationship meaningful when it is statistically significant at the 0.05 level. To begin, Varden collects values for ROE, CEO tenure, and ESG rating for a sample of 40 companies from the large-cap security universe. He performs a multiple regression with ROE (in percent) as the dependent variable and ESG rating and CEO tenure (in years) as the independent variables: Y,= b + b Xu + b2X2 + Exhibit 1 shows the regression results. EXHIBITI Regression Statistics Y = 9.442 + 0.069X+0.681X31 Coefficient Standard Error p-Value Intercept 9.442 3.343 (ESG variable) 0.069 0.058 bz (Tenure variable) 0.681 0.295 ANOVA DF SS MSS Significance F Regression 240.410 4.161 0.023 Residual 1069.000 Total 1309.410 Multiple R R Adjusted R Sandard error (%) Observations DF Associates is one of the companies Varden follows. He wants to predict its ROE using his regression model. DF Associates' corporate ESG rating is 55, and the company's CEO has been in that position for 10.5 years. Varden also wants to check on the relationship between these variables and the dividend growth rate (divgr), so he completes the correlation matrix shown in Exhibit 2. 0.008 2.824 1.201 2.308 0.238 0.027 F 2 120.205 28.892 37 39 0.428 0.183 0.139 5.375 40 EXHIBIT 2 Correlation Matrix ESG Tenure ROE Divgr ROE ESG Tenure Divgt 1.0 0.446 0.369 0.117 1.0 1.0 0.091 0.046 0.028 1.0 Quantitative Investment Analysis 448 Investigating further , Varden determines that dividend growth is not a linese combination of CEO tenure and Esg rating. He is unclear about how additional independent variables would affect the significance of the regression, so he asks Quinni, "Given this correlation matrix, will both R and adjusted R automatically increase if I add dividend growth as a third independent variable?" The discussion continues, and Quinni asks two questions. 1. What does your F-statistic of 4.161 tell you about the regression? 2. In interpreting the overall significance of your regression model , which statistic do you believe is most relevant: R', adjusted Re", or the F-statistic? Varden answers both questions correctly and says he wants to check two more ideas. He believes the following: 1. ROE is less correlated with the dividend growth rate in firms whose CEO has been in office more than 15 years, and 2. CEO tenure is a normally distributed random variable. Later, Varden includes the dividend growth rate as a third independent variable and runs the regression on the fund's entire group of 500 large-cap equities. He finds that the adjusted R is much higher than the results in Exhibit 1. He reports this to Quinni and says, "Adding the dividend growth rate gives a model with a higher adjusted R. The three-variable model is clearly better." Quinni cautions, I don't think you can conclude that yet." 37. Based on Exhibit 1 and given Varden's expectations, which is the best null hypothesis and conclusion regarding CEO tenure? A. 62 S 0; reject the null hypothesis B. by = 0; cannot reject the null hypothesis C. b2 2 0; reject the null hypothesis 38. At a significance level of 1%, which of the following is the best interpretation of the regression coefficients with regard to explaining ROE? A. ESG is significant, but tenure is not. B. Tenure is significant, but ESG is not. C. Neither ESG nor tenure is significant. 39. Based on Exhibit 1, which independent variables in Varden's model are significant at the 0.05 level? A. ESG only B. Tenure only C. Neither ESG nor tenure 40. Based on Exhibit 1, the predicted ROE for DF Associates is closest to: A. 10.957%. B. 16.593%. C. 20.388%. 41. Based on Exhibit 2, Quinni's best answer to Varden's question about the effect of adding a third independent variable is: A.no for R and no for adjusted R. B. yes for R and no for adjusted R. C. yes for R and yes for adjusted R. Chapter 8 Multiple Regression 449 42. Based on Exhibit 1, Varden's best answer to Quinni's question about the F-statistic is: A. both independent variables are significant at the 0.05 level. B. neither independent variable is significant at the 0.05 level. C. at least one independent variable is significant at the 0.05 level. 43. Varden's best answer to Quinni's question about overall significance is: A. R. B. adjusted R. C. the F-statistic. 44. If Varden's beliefs about ROE and CEO tenure are true, which of the following would violate the assumptions of multiple regression analysis? A. The assumption about CEO tenure distribution only B. The assumption about the ROE/dividend growth correlation only C. The assumptions about both the ROE/dividend growth correlation and CEO tenure distribution 45. The best rationale for Quinni's caution about the three-variable model is that the: A. dependent variable is defined differently. B. sample sizes are different in the two models. C. dividend growth rate is positively correlated with the other independent variables