Skip to content

IAI Actuarial Core Principles · Actuarial Statistics · Linear regression models

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 one used to derive the exact t-based inference for b?

The standard assumption is that the errors are independent, identically distributed normal with mean zero and constant variance sigma squared. This gives exact t-distributions for the slope estimator. The other options introduce heteroscedasticity, correlation or non-zero means.

  1. Ae_i are independent and identically distributed N(0, sigma^2)Correct
  2. Be_i are independent N(0, sigma^2 x_i^2), with variance proportional to x_i^2
  3. Ce_i are independent with mean 1 and common variance sigma^2
  4. De_i are N(0, sigma^2) with Cov(e_i, e_j) = sigma^2/2 for all i not equal to j
  5. e_i are N(mu, sigma^2) with mu depending on x_i

Explanation

The classical normal linear model assumes errors with zero mean, constant variance, independence and normality. Option B is heteroscedastic, C has a non-zero mean, D has correlated errors and E has a mean that depends on x, so none of those supports the exact t-inference.

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