2. (29 points) An analyst intends to investigate the relationship between bond yield spread and firm profitability. Bond yield spread is measured as the bond yield to maturity minus LIBOR (London Interbank Offered Rate, which is treated as a benchmark). Bond yield spread (Dependent variable Y: Spread) is measured as basis points (see Hint [1]). Firm profitability is measures as ROA (Independent Variable X: ROA), which is Return on Assets. Hint [1]: 1 basis point is corresponding to one hundredth of a percentage point (0.01%). Basis points are often used to measure changes in or differences between yields on fixed income securities, since these often change by very small amounts. For example, Bond-ID 1, the spread is 26 basis points, which is 26*0.01%=0.26% Net Income Hint [2]: ROA= x 100 Assets For example, Bond-ID 1, the ROA is actually 10.16%. However, in the regression analysis, 10.16 is used as the entry of independent variable. Hint [3]: X(X - XN? = 751.8506 Hint [4]: sample size is 30 A portion of the data is shown as follows so that you can understand how Spread and ROA are measured. BOND-ID SPREAD ROA 1 26 10.16 2 30 7.79 3 32 19.81 4 33 19.99 5 34 20.14 6 34 20.65 7 35 10.84 8 40 9.62 45 3.31 10 45 9.01 SUMMARY OUTPUT Dependent variable: Spread Regression Statistics R Square j Standard Error 17.2188 9 ANOVA df F i a Regression Residual Total sum of squares f 8301.6474 11724.1666 mean squares g h b Coefficients 126.8928 -2.1335 Intercept ROA Standard Error 4.45528 d t Stat 28.4814 e (1) Complete all the missing values (Marked with lower letters in Bold and Italic) in the following table. (15 points-1.5 points each) b d a e f g h i j (2) What is the estimated regression equation relating Bond Yield Spread to firm profitability (ROA)? (2 points) (3) How to interpret the coefficient of ROA? (2 points) (4) Suppose a company's ROA is 11.26%, what will be your predication of the Bond Yield Spread according to the above estimated regression function? (2 points) (5) What percentage of the variance in Bond Yield Spread has been explained by the regression? Is this percentage significant at a= 0.05?(2 points) (6) Construct a 95% confidence interval for B. (3 points) (7) A proposal is made that o can be estimated by SSTO/(n-1). Why is this estimate not appropriate and why is MSE a better estimator? (3 points) 2. (29 points) An analyst intends to investigate the relationship between bond yield spread and firm profitability. Bond yield spread is measured as the bond yield to maturity minus LIBOR (London Interbank Offered Rate, which is treated as a benchmark). Bond yield spread (Dependent variable Y: Spread) is measured as basis points (see Hint [1]). Firm profitability is measures as ROA (Independent Variable X: ROA), which is Return on Assets. Hint [1]: 1 basis point is corresponding to one hundredth of a percentage point (0.01%). Basis points are often used to measure changes in or differences between yields on fixed income securities, since these often change by very small amounts. For example, Bond-ID 1, the spread is 26 basis points, which is 26*0.01%=0.26% Net Income Hint [2]: ROA= x 100 Assets For example, Bond-ID 1, the ROA is actually 10.16%. However, in the regression analysis, 10.16 is used as the entry of independent variable. Hint [3]: X(X - XN? = 751.8506 Hint [4]: sample size is 30 A portion of the data is shown as follows so that you can understand how Spread and ROA are measured. BOND-ID SPREAD ROA 1 26 10.16 2 30 7.79 3 32 19.81 4 33 19.99 5 34 20.14 6 34 20.65 7 35 10.84 8 40 9.62 45 3.31 10 45 9.01 SUMMARY OUTPUT Dependent variable: Spread Regression Statistics R Square j Standard Error 17.2188 9 ANOVA df F i a Regression Residual Total sum of squares f 8301.6474 11724.1666 mean squares g h b Coefficients 126.8928 -2.1335 Intercept ROA Standard Error 4.45528 d t Stat 28.4814 e (1) Complete all the missing values (Marked with lower letters in Bold and Italic) in the following table. (15 points-1.5 points each) b d a e f g h i j (2) What is the estimated regression equation relating Bond Yield Spread to firm profitability (ROA)? (2 points) (3) How to interpret the coefficient of ROA? (2 points) (4) Suppose a company's ROA is 11.26%, what will be your predication of the Bond Yield Spread according to the above estimated regression function? (2 points) (5) What percentage of the variance in Bond Yield Spread has been explained by the regression? Is this percentage significant at a= 0.05?(2 points) (6) Construct a 95% confidence interval for B. (3 points) (7) A proposal is made that o can be estimated by SSTO/(n-1). Why is this estimate not appropriate and why is MSE a better estimator? (3 points)