FRM Part I · FRM Exam Part I · Regression with Multiple Explanatory Variables
A risk analyst regresses monthly excess returns of a fund on three explanatory factors using 60 observations. The regression has a total sum of squares (TSS) of 400 and a residual sum of squares (RSS) of 100. What is the R-squared of the regression?
R-squared is one minus the ratio of residual sum of squares to total sum of squares. Here that is 1 - 100/400 = 0.75, so the three factors explain 75 percent of the variation in fund excess returns. The value 0.25 is the unexplained share.
- A0.25
- B0.75Correct
- C0.33
- D1.33
Explanation
R-squared = 1 - RSS/TSS = 1 - 100/400 = 0.75. The value 0.25 is the unexplained fraction RSS/TSS, which is the complement of R-squared. The value 0.33 comes from dividing ESS by RSS (300/100 = 3) incorrectly or using other ratios, and 1.33 is TSS/ESS, so neither is correct.
Did you get it right without looking?
One question tells you little. A timed set on Regression with Multiple Explanatory Variables shows your real accuracy, how long you take and where you lose marks.
More Regression with Multiple Explanatory Variables questions
- A regression of bond yield spread on leverage (L) and a crisis dummy D (1 during crisis) with an interaction is: Spread = 40 + 30*L + 25*D +…
- An analyst regresses monthly excess returns of a fund on the market excess return and a dummy variable D that equals 1 for months in which t…
- An analyst regresses a stock's return on two factors, X1 and X2. An auxiliary regression of X1 on X2 (with an intercept) gives an R-squared …
- In a two-regressor model, the standard error of the slope on X1 is 0.30 when X1 and X2 are correlated with an auxiliary R-squared of 0.75. H…
- A analyst omits a relevant explanatory variable X2 from a regression of returns on X1. X2 has a positive true effect on returns and is posit…
- A researcher models bond spread changes using quarterly data and wants to capture seasonal effects with an intercept for each of the four qu…