Question

In a simple linear regression model, the ANOVA F test is a test of model significance (i.e. a test of whether the linear regression model is significantly better than the trivial model y_i = β₀ + ε_i). This test can be performed in another way (i.e. by the 'extra sum of squares' or ESS method considering the simple linear regression model as the 'full model' and the trivial model y_i = β₀ + ε_i as the 'reduced model'). There is also a student's t test for testing: H₀: β₁ = 0 vs H₁: β₁ ≠ 0. Write down the test statistics for all 3 tests and show that these 3 tests are algebraically equivalent.

Answer 1