FRM Part I · FRM Exam Part I · Regression Diagnostics
Which of the following is an example of perfect multicollinearity that would prevent OLS from producing a unique solution?
Including all four quarterly dummy variables together with an intercept creates perfect multicollinearity, because the dummies sum to one in every observation and duplicate the intercept column. OLS then has no unique solution. A variable and its square, or a 0.95 correlation, are not exact linear dependencies.
- AIncluding both a variable and its square as regressors
- BIncluding dummy variables for all four quarters together with an interceptCorrect
- CIncluding two regressors with a correlation of 0.95
- DIncluding a regressor with a correlation of -0.60 with the error term proxy
Explanation
Four quarterly dummies sum to one for every observation, which is exactly the intercept column, creating an exact linear dependence (the dummy variable trap). A variable and its square are nonlinearly related, so not perfectly collinear. A correlation of 0.95 is high but not perfect.
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
- In a cross-sectional regression of household food spending on household income, the dispersion of the residuals grows steadily as income ris…
- A risk manager estimates a time-series regression by OLS and finds the residuals are positively autocorrelated, while the regressors are not…
- After fitting a multiple regression, an analyst finds that a plot of residuals against a regressor shows a systematic U-shaped pattern. Whic…
- In a multiple regression of a fund's excess return on several factor returns, an analyst finds that the R-squared is high and the F-test is …
- A risk analyst is concerned about severe multicollinearity between two regressors, X1 and X2, in a model used to forecast portfolio losses. …
- A regression of y on x gives a slope of 2.00 with a conventional standard error of 0.50. After applying heteroskedasticity-robust (White) st…