FRM Part I · FRM Exam Part I · Regression with Multiple Explanatory Variables
A model of credit spreads is first estimated with 3 explanatory variables on 60 observations, giving a residual sum of squares (RSS) of 48. Adding 2 further variables lowers RSS to 40. Testing whether the 2 added coefficients are jointly zero, the F-statistic is closest to which value?
The F-statistic is about 5.4, closest to 5.5. It equals the reduction in residual sum of squares per restriction, (48-40)/2 = 4, divided by the unrestricted residual variance, 40/54 = 0.741, where 54 is 60 observations minus 6 estimated coefficients.
- A5.5Correct
- B4.0
- C6.6
- D2.2
Explanation
Restricted model: 3 variables plus intercept. Unrestricted has 5 variables plus intercept, so df = 60-6 = 54. F = [(48-40)/2]/[40/54] = 4/0.7407 = 5.4, about 5.5. Using 56 df or other mistakes gives other values; 4.0 omits the denominator scaling.
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
- 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 researcher models bond spread changes using quarterly data and wants to capture seasonal effects with an intercept for each of the four qu…
- A researcher estimates an unrestricted regression with 5 explanatory variables and an intercept on 124 observations, getting R-squared of 0.…
- In a multiple regression, the standard error of a slope coefficient would be 0.040 if its regressor were uncorrelated with the other regress…
- A risk manager models quarterly loss rates using an intercept and three seasonal dummy variables (Q2, Q3, Q4) with Q1 as the base period, an…
- A regression of bond spread on leverage (L) and a rating-group dummy D (1 = speculative grade) with an interaction term gives: Spread = 80 +…