How can we check whether coefficeints of a multivariable regression models are zero(null hypothesis) without creating full and restricted model?

Question

I want to test whether a variable Y has an influence over other variable Y. For this I have established a null hypothesis that the coefficients of Y in the regression model are zero. Can I test this hypothesis without having a need to create Full or Restricted model, so as to make it computationally less expensive ? If yes please explain me how this can be achieved.

Answer 1

In linear regression this is called the t-test, i.e. your test statistic is the coefficient divided by its standard error, and you compare it with a t-distribution with the residual degrees of freedom. Any introductory statistics test covering linear regression will be able to provide you all the details.