If our regression model has K predictors, the “alternative model” is described using the usual formula for a multiple regression model: Formally, our “null model” corresponds to the fairly trivial “regression” model in which we include 0 predictors, and only include the intercept term b 0 The first hypothesis test you might want to try is one in which the null hypothesis that there is no relationship between the predictors and the outcome, and the alternative hypothesis is that the data are distributed in exactly the way that the regression model predicts. Okay, suppose you’ve estimated your regression model. In fact, all I’m going to do in this section is show you how those tests are imported wholesale into the regression framework. I’m so sick of hypothesis tests that I’m going to shamelessly reuse the F-test from Chapter 14 and the t-test from Chapter 13. You’re probably sick of hypothesis tests by now, and don’t want to learn any new ones. There are two different (but related) kinds of hypothesis tests that we need to talk about: those in which we test whether the regression model as a whole is performing significantly better than a null model and those in which we test whether a particular regression coefficient is significantly different from zero.Īt this point, you’re probably groaning internally, thinking that I’m going to introduce a whole new collection of tests. The next thing we need to talk about is hypothesis tests.

So far we’ve talked about what a regression model is, how the coefficients of a regression model are estimated, and how we quantify the performance of the model (the last of these, incidentally, is basically our measure of effect size).

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