What Is the F | f test significance level
Previously,I’vewrittenabouthowtointerpretregressioncoefficientsandtheirindividualPvalues[1].I’vealsowrittenabouthowtointerpretR-squared[2]toassessthestrengthoftherelationshipbetweenyourmodelandtheresponsevariable.RecentlyIvebeenasked,howdoestheF-testoftheoverallsignificanceanditsPvaluefitinwiththeseotherstatistics?That’sthetopicofthispost!Ingeneral,anF-testinregressioncomparesthefitsofdifferentlinearmodels.Unliket-teststhatcanassessonlyoneregressioncoefficientatatime,theF-testcanassessmultip...
Previously, I’ve written about how to interpret regression coefficients and their individual P values[1].
I’ve also written about how to interpret R-squared[2] to assess the strength of the relationship between your model and the response variable.
Recently Ive been asked, how does the F-test of the overall significance and its P value fit in with these other statistics? That’s the topic of this post!
In general, an F-test in regression compares the fits of different linear models. Unlike t-tests that can assess only one regression coefficient at a time, the F-test can assess multiple coefficients simultaneously.
The F-test of the overall significance is a specific form of the F-test. It compares a model with no predictors to the model that you specify. A regression model that contains no predictors is also known as an intercept-only model.
The hypotheses for the F-test of the overall significance are as follows:
Null hypothesis: The fit of th...