CFA Level IQuantitative MethodsHard
A regression of a stock's monthly returns on market index returns produces the equation: Stock Return = 0.5% + 1.2 x (Market Return), with an R-squared of 0.64. What is the correlation coefficient between the stock's returns and the market's returns?
- A0.80
- B0.40
- C1.20
- D0.64
Show answer & explanationAnswer & explanation
Correct answer: A. 0.80
For simple linear regression with one independent variable, R-squared equals the square of the correlation coefficient. Since the slope coefficient is positive, r = sqrt(0.64) = 0.80.
Why the other options are wrong
- B. This understates the correlation; it does not correspond to any correct calculation from the given data.
- C. This is the slope coefficient (beta), not the correlation coefficient.
- D. This is R-squared itself, not the correlation coefficient.
R-Squared and Correlation
In simple linear regression, R-squared represents the proportion of variation in the dependent variable explained by the independent variable and equals the square of the correlation coefficient between the two variables.
- R^2 = r^2 in simple (one-variable) linear regression
- r = sqrt(R^2), with sign matching the slope coefficient's sign
- R^2 ranges from 0 to 1; higher values indicate better model fit
Memory trick: Square root R-squared, borrow the slope's sign.