Using R for Introductory Statistics : John Verzani

Using R for introductory statistics 276(10.4)The standard errors are found from the known formulas for the variances of the(10.5)(Recall that,Marginal t-testsWe can find confidence intervals and construct significance tests from the statistics in(10.4) and (10.5). For example, a significance test forH 0 :β 1 =b, H A :β 1 ≠bis carried out with the test statisticUnder H 0 , T has the t-distribution with n−2 degrees of freedom.A similar test for β 0 would use the test statisticWhen the null hypothesis is β 1 =0 or β 0 =0 we call these marginal t-tests, as they testwhether the parameter is necessary for the model.The F-testAn alternate test for the null hypothesis β 1 =0 can be done using a different but relatedapproach that generalizes to the multiple-regression problem.Figure 10.6 The plot on the leftshows regression lines for 100simulations from the model Y i =x i +ε i .The plotted points show a singlerealization of the paired data during