# F-test explained in laymans terms

by jprockbelly
Tags: explained, ftest, laymans, terms
 HW Helper P: 1,361 Remember that in regression you're investigating whether the independent variables provide any useful information for you to use in the prediction of the mean value of Y (this is a simplified comment, but we're talking about linear regression so it works). The basic hypotheses for the F-test are \begin{align*} H_0 \colon & \beta_1 = \beta_2 = 0 \\ H_a \colon & \text{At least one coefficient is not zero} \end{align*} If the null hypothesis is true you're left with the result that the best way to estimate the mean value of Y is with the ordinary sample mean. If the alternative hypothesis is true then you can say your data indicates the mean value of Y is not constant but varies in a way consistent with your model. In short: the F-test provides a way to distinguish which of two models (constant mean vs variable mean) best describes the variable Y.