What is the difference between the t-test for slope coefficient and the f-test?
In the curriculum it says that the f-test is a test of whether all slope coefficients in a regression equal 0, and the t-test for the slope coefficient tests a hypothesis that the slope coefficient equals 1 (beta).
What is the difference between these two approaches?
The F-test, as you say, tests whether or not all of the slopes are zero simultaneously. If so, the model is worthless; if not – i.e., if at least one of the slopes is not zero – then the model may be useful. If it shows that not all of the slopes are zero, it, unfortunately, doesn’t give any indication which slope or slopes are nonzero, only that one or more are.
The individual t-tests check each slope coefficient separately. Furthermore, you can check whether or not each slope coefficient equals any particular value; that value doesn’t have to be zero.
Thanks a lot!!!
My pleasure.