Skip to content

IAI Actuarial Core Principles · Actuarial Statistics · Linear regression models

A regression with an intercept and two covariates is fitted to n = 20 observations. The estimated variance σ̂² = 4 and the relevant diagonal element of (XᵀX)⁻¹ for β₁ is 0.25. Given β̂₁ = 2.5, what is the value of the t statistic for testing H₀: β₁ = 0?

The t statistic is 2.50. The estimated variance of β̂₁ is σ̂² times the diagonal element, 4 × 0.25 = 1, so the standard error is 1. Dividing the estimate 2.5 by 1 gives 2.5, tested on 17 degrees of freedom.

  1. A1.25
  2. B2.50Correct
  3. C5.00
  4. D10.00
  5. 2.00

Explanation

Var(β̂₁) = σ̂² × 0.25 = 4 × 0.25 = 1, so the standard error is 1. The t statistic is 2.5/1 = 2.5, compared with t on 17 degrees of freedom. Using 0.25 as the standard error gives 10, which is a mistake.

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.

Practise Linear regression modelsFree diagnostic mock

More Linear regression models questions