Thread: Hypothesis tests for regression coefficients

Hey,

doing a question on hypothesis testing for regression coefficients and a formula I have to work out the t value is t = (β - b)/root( σ²(X'X)^-1_jj) for my beta I have 0.04399 and for sigma squared I have 0.0215 and for (X'X)^-1 I have ( 0.28553 -0.0058 0.00713; -0.0058 0.00013 -0.00019; 0.00713 -0.00019 0.00047) the only thing I'm struggling with is understanding how to calculate (σ² * (X'X)₃₃ ) don't really know how to calculate the matrix bit really, all I know is it's the diagonal element. Any help appreciated thanks!

Nathan

Hey NathanBUK.

Just calculate the transpose of the matrix X (which is X') and then multiply this by X and you should get a covariance estimate matrix which you can use for inference.