**Unformatted text preview: **regression coeﬃcient of Y on e ( X k | X 1 , · · · , X k − 1 , X k +1 , · · · , X p − 1 ). There-fore, the multiple regression coeﬃcient ˆ β k represents the additional contribu-tion of X k on Y , after X k has been adjusted for 1 , X 1 , · · · , X k − 1 , X k +1 , · · · , X p − 1 . 1 > m1.23<-lm(x1~x2+x3) > summary(lm(y~resid(m1.23))) Call: lm(formula = y ~ resid(m1.23)) Residuals: Min 1Q Median 3Q Max-9.6795 -2.8254 0.4596 3.4210 7.6207 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 20.195 1.158 17.441 1.01e-12 *** resid(m1.23) 4.334 6.297 0.688 0.5---Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 Residual standard error: 5.178 on 18 degrees of freedom Multiple R-squared: 0.02565, Adjusted R-squared: -0.02848 F-statistic: 0.4738 on 1 and 18 DF, p-value: 0.5 2...

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- Fall '19