The F test tests that all coefficients are significant at the 95% say significance level. If a t test is run on one of the coefficients at the 95% level of confidence then if another t test of significance is run at the 95% level we now can no longer say that we are 95% confident and we are less and less confident each time we run another t-test. Running a single F test for all coefficients will test if the model is adequate without losing any confidence.

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