FRM Part I · FRM Exam Part I · Regression Diagnostics
A regression coefficient on variable X has a standard error of 0.040 when X is uncorrelated with the other regressors. After adding other regressors, the auxiliary regression of X on those regressors has an R-squared of 0.84, with all else unchanged. What is the approximate new standard error of X's coefficient?
The new standard error is about 0.100. The auxiliary R-squared of 0.84 gives a VIF of 6.25, and standard errors scale with the square root of the VIF, which is 2.5. Multiplying 0.040 by 2.5 gives 0.100.
- A0.100Correct
- B0.160
- C0.250
- D0.064
Explanation
VIF = 1/(1-0.84) = 6.25. The standard error scales with the square root of the VIF: sqrt(6.25) = 2.5. New standard error = 0.040 × 2.5 = 0.100. Multiplying by the VIF itself would give 0.250, which is the common error.
Did you get it right without looking?
One question tells you little. A timed set on Regression Diagnostics shows your real accuracy, how long you take and where you lose marks.
More Regression Diagnostics questions
- A risk manager adds several irrelevant explanatory variables to a correctly specified regression that already includes all relevant variable…
- An analyst plots residuals of a time-series regression in date order and sees long runs of positive residuals followed by long runs of negat…
- An analyst runs a Breusch-Pagan test by regressing the squared residuals from an original model on the model's 3 explanatory variables. The …
- An analyst finds two regressors in a model with a pairwise correlation of 0.95 and considers remedies. Which action is most appropriate to r…
- An analyst regresses monthly excess returns of a fund on the market excess return and plots the residuals against the fitted values. The plo…
- In a linear regression estimated by OLS, the error variance rises with the size of an explanatory variable, but the model is otherwise corre…