AIMs: Define and interpret the explained sum of squares (ESS), the total sum of squares (TSS), the sum of squared residuals (SSR), the standard error of the regression (SER), and the regression R^2.
Questions:
216.1. For the last three years, we regressed monthly dollar change in gasoline prices (regressand; dependent) against the monthly change in oil prices (regressor; independent). The number of observations (n) is therefore 36. If the coefficient of determination (R^2) is 0.18 and the total sum of squares (TSS) is 3.23 dollars^2, what is the standard error of the regression (SER)?
a. $0.28
b. $0.42
c. $2.65
d. $3.23
216.2. We regressed daily returns of a stock (the regressand or dependent variable) against a market index (e.g., S&P 1500; regressor or independent variable). The regression produced a beta for the stock, with respect to the market index, of 1.050. The stock's volatility was 30.0% and the market's volatility was 20.0%. If the regression's total sum of squares (TSS) is 0.300, what is the regression's explained sum of squares (ESS)?
a. 0.0960
b. 0.1470
c. 0.4900
d. 1.2500
216.3. A five-year regression of monthly cotton price changes, such that the number of observations (n) equals 60, against average temperature changes produced a standard error of the regression (SER) of $1.20. If the total sum of squares (TSS) was $90.625 dollars^2 , what is the implied correlation coefficient?
a. 0.08
b. 0.16
c. 0.28
d. 0.77
Answers:
Questions:
216.1. For the last three years, we regressed monthly dollar change in gasoline prices (regressand; dependent) against the monthly change in oil prices (regressor; independent). The number of observations (n) is therefore 36. If the coefficient of determination (R^2) is 0.18 and the total sum of squares (TSS) is 3.23 dollars^2, what is the standard error of the regression (SER)?
a. $0.28
b. $0.42
c. $2.65
d. $3.23
216.2. We regressed daily returns of a stock (the regressand or dependent variable) against a market index (e.g., S&P 1500; regressor or independent variable). The regression produced a beta for the stock, with respect to the market index, of 1.050. The stock's volatility was 30.0% and the market's volatility was 20.0%. If the regression's total sum of squares (TSS) is 0.300, what is the regression's explained sum of squares (ESS)?
a. 0.0960
b. 0.1470
c. 0.4900
d. 1.2500
216.3. A five-year regression of monthly cotton price changes, such that the number of observations (n) equals 60, against average temperature changes produced a standard error of the regression (SER) of $1.20. If the total sum of squares (TSS) was $90.625 dollars^2 , what is the implied correlation coefficient?
a. 0.08
b. 0.16
c. 0.28
d. 0.77
Answers:
