(1 + 2^-52) - 1 (1 + 2^-53) - 1 .Machine$double.eps 2^-52 x <- 0.1 + 0.2 - 0.3 x x == 0 isTRUE(all.equal(x, 0)) abs(x) < 1e-12 sqrt(.Machine$double.eps) all.equal(list(), 7) isTRUE(all.equal(list(), 7)) A<-matrix(c(1,2,2,1),2,2) b<-matrix(c(1,1),2,1) x <- solve(A) %*% b A %*% x data(trees) head(trees) nrow(trees) pairs(trees) lm1 <- lm(Volume ~ Height + Girth, data=trees) summary(lm1) X = cbind(1, trees$Height, trees$Girth) beta = qr.solve(X, trees$Volume) beta