Mathematics · Linear Regression
An analyst fits a multiple linear regression model Yi = β0 + β1X1i + β2X2i + β3X3i + β4X4i + εi, i = 1,2,...,n, using the method of least squares. A coordinator claims that under restrictions, a reduced model is sufficient, which can be expressed as a linear hypothesis H0: LTβ = 0 where LT is a 2 × 5 matrix testing two linear independent constraints. If the errors are independent N(0, σ2) variables, what is the distribution of the test statistic for testing H0 against HA?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1It follows a central F-distribution with (2, n - 4) degrees of freedom under H0.
- 2It follows a Chi-square distribution with n - 2 degrees of freedom.
- 3It follows an F-distribution with (2, n - 5) degrees of freedom under H0.✓
- 4It follows a central t-distribution with n - 5 degrees of freedom under H0.
Correct answer
It follows an F-distribution with (2, n - 5) degrees of freedom under H0.
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