IAI Actuarial Core Principles · Actuarial Statistics · Linear regression models
A researcher adds a further explanatory variable to a fitted linear regression model with an intercept. Which statement is certainly true?
R² cannot decrease when a variable is added, because least squares can always reproduce the earlier fit by setting the new coefficient to zero, so SSE does not rise. Adjusted R² and F may fall, and residual degrees of freedom decrease.
- AR² cannot increase
- BR² cannot decreaseCorrect
- CAdjusted R² cannot decrease
- DThe residual degrees of freedom increase
- The F statistic must increase
Explanation
Adding a variable can never raise SSE under least squares, since the earlier model is a special case with coefficient zero, so R² cannot decrease. Adjusted R² can fall because of the df penalty, residual df decrease by one, and F can fall.
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
- 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…
- For a simple linear regression with n = 10 observations, x̄ = 4, ȳ = 30, Sxx = 40 and Sxy = 100. The fitted line is used to predict y at x =…
- A regression through five points gives residual sum of squares 18 for the model y = α + βx + ε with errors N(0, σ²). What is the unbiased es…
- A simple linear regression with n = 14 has residual standard error s = 4, mean x of 10, and Sxx = 200. At x0 = 14 the fitted value is 50. Wh…
- In a simple linear regression fitted to n = 12 observations, the estimated slope is 2.50 with standard error 0.80. For a test of H0: slope =…
- A multiple regression with k = 3 explanatory variables is fitted to n = 24 observations. R² = 0.80. What is the adjusted R²?