For the population of chief executive officers (CEO), let salary be annual salar
ID: 3261472 • Letter: F
Question
For the population of chief executive officers (CEO), let salary be annual salary in millions of dollars, and let roe be the average return on equity for the previous three years. Return on equity (roe) is defined in terms of net income as a percentage of common equity. For example, if roe=10, then average return on equity is 10%. Using the data, the OLS regression line relating salary to roe is salary = 1.25 + 0.33roe n = 209, R^2 = 0.213 (a) Interpret the intercept clearly (b) Interpret the slope estimate clearly (c) What is the predicted salary when roe=25? (d) Explain the meaning of R^2 = 0.213 clearlyExplanation / Answer
1. (a) Intercept is that value of y(dependent variable) when the value of x(independent variable) is 0.
Hence, in this case, when Return on equity(ROE) is 0 salary is 1.25 million dollars. (Ans).
(b) Slope is the change in y-value for a unit change in x-value.
Hence, in this case, if Return on equity(ROE) changes(increases or decreases) by 1 unit, Salary will change(increase or decrease) by an amount of 0.33 million dollars. (Ans).
(c) When ROE = 25, from the regression equation we get, y = 1.25 + (0.33*25) = 9.5.
Hence the predicted salary is 9.5 million dollars when ROE is 25 units. (Ans).
(d) R-square implies the proportion of variation in y (dependent variable) explained by x (independent variable).
R-square = 0.213 implies 21.3% of variation in salary is explained by ROE. (Ans).