7 y1 20 lmy x1 x2 x1 07 x2 44 point

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Unformatted text preview: gt; lm(y ~ x1 + x2) Call: lm(formula = y ~ x1 + x2) Coefficients: (Intercept) 3.7 > y[1] = 20 > lm(y ~ x1 + x2) x1 -0.7 x2 4.4 ### point 1 has large leverage Call: lm(formula = y ~ x1 + x2) Coefficients: (Intercept) 8.875 x1 -1.375 x2 4.625 > y[1] = 11 > y[4] = 30 > lm(y ~ x1 + x2) ### point 4 has small leverage Call: lm(formula = y ~ x1 + x2) Coefficients: (Intercept) 5.7 x1 -0.7 x2 4.4 > mean(x1); mean(x2) [1] 7 [1] 3 Example 3: > > > > > > > > > > x1 = c(5,4,3,0,-3,-4,-5,-4,-3,0,3,4) x2 = c(0,3,4,5,4,3,0,-3,-4,-5,-4,-3) par(pty="s") ### square plot plot(x1,x2) points(0,0,pch=3) X = cbind(rep(1,12),x1,x2) H = X %*% solve(t(X)%*%X) %*% t(X) lev = rep(0,12) for (i in 1:12) lev[i]=H[i,i] lev [1] 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 > sum(lev) [1] 3 ˆ e=Y– Y = ( – ) Y. Var ( e i ) = ri = Studentized residuals: Cook’s Distance: Di = 1 p ri2 ei s 1 − hi hi , 1 − hi , ( 1 – h i ) σ 2. i = 1, 2, … , n. i = 1, 2, … , n. measures the influence of a data point on the regression equation....
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This note was uploaded on 04/03/2014 for the course STAT 420 taught by Professor Stepanov during the Spring '08 term at University of Illinois, Urbana Champaign.

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