FRM Part I · FRM Exam Part I · Regression Diagnostics
In a simple regression with n = 25 observations, one observation has a standardized (studentized) residual of 3.4, but its leverage is very low. Compared with an observation with a moderate residual and very high leverage, how should the first observation be described?
The observation is a y-direction outlier with low leverage, so its influence on the fitted slope is small. Influence needs both a large residual and high leverage. A large residual alone does not justify automatic deletion; the data point should be investigated first.
- AIt is an outlier in the y-direction with low influence, so it has little effect on the fitted slopeCorrect
- BIt has high leverage and high influence because its residual is large
- CIt is not an outlier because leverage is low
- DIt must be removed because any residual above 3 invalidates the regression
Explanation
A large studentized residual with low leverage means the point is unusual in y given x but sits near the mean of x, so it pulls the fitted line little. Influence depends on both residual size and leverage. Automatic deletion is not justified; the observation should be investigated.
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
- 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 regression with n = 50 observations and k = 4 explanatory variables (plus an intercept), one observation has leverage h = 0.30. Using t…
- An analyst regresses a stock's returns on market returns using 50 observations. She runs a Breusch-Pagan style auxiliary regression of the s…