Question

In a multiple linear regression y = β₀ + β₁x₁ + β₂x₂ + β₃x₃, based on two-tailed t tests, if β₁ is not significant, but β₂ and β₃ are significant, what shall we do the next?

Answer 1

In a multiple linear regression y = β0 + β1x1 + β2x2 + β3x3, based on two-tailed t tests, if β1 is not significant, but β2 and β3 are significant we shall discard the independent variable x1 and carry our regression analysis with only two independent variable x2 and x3.

If β1 comes out to be insignificant, it means that not much of the variability of y is explained by x1 and hence including x1 in our study won’t be much necessary furthermore including x1 will complicate our calculations. Hence it is better to discard x1.