IAI Actuarial Core Principles · Actuarial Statistics · Linear regression models
In a multiple regression with p = 4 parameters (including intercept) and n = 20 observations, one observation has standardised residual r = 2.0 and leverage h = 0.25. Using Cook's distance D = r^2 * h / (p(1-h)), what is D?
Cook's distance is about 0.33. Substituting gives 4 times 0.25 divided by 4 times 0.75, which is 1 divided by 3. The distance is below 1, so the observation is not usually flagged as highly influential by the common rule of thumb.
- A0.25
- B0.33Correct
- C0.50
- D1.00
- 1.33
Explanation
D = 4 * 0.25 / (4 * 0.75) = 1/3 = 0.333. Using h instead of h/(1-h) gives 0.25, a distractor. Using r^2 h/p without the (1-h) denominator gives 0.25 also. Dropping the p divisor gives 1.33.
Did you get it right without looking?
One question tells you little. A timed set on Linear regression models shows your real accuracy, how long you take and where you lose marks.
More Linear regression models questions
- A simple linear regression with an intercept is fitted to n = 12 observations. The residual sum of squares is 90 and the leverage of one obs…
- In a simple linear regression fitted to n = 12 observations, the estimated slope is 2.50 with standard error 0.80. Using the t-distribution …
- A simple linear regression of y on x is fitted by least squares to n = 20 observations. The summary statistics are Sxx = 50, Sxy = 120 and S…
- In a simple linear regression fitted by least squares with an intercept, which statement about the raw residuals e_i = y_i - fitted y_i is a…
- In a simple linear regression with n = 27 observations, the total sum of squares is 500 and the regression sum of squares is 300. What is th…
- In the simple linear regression model Y_i = a + b x_i + e_i, which one of the following sets of assumptions on the errors is the standard on…