tasks a-s

Task/QR-decomposition/R/qr-decomposition.r

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+# R has QR decomposition built-in (using LAPACK or LINPACK)
+
+a <- matrix(c(12, -51, 4, 6, 167, -68, -4, 24, -41), nrow=3, ncol=3, byrow=T)
+d <- qr(a)
+qr.Q(d)
+qr.R(d)
+
+# now fitting a polynomial
+x <- 0:10
+y <- 3*x^2 + 2*x + 1
+
+# using QR decomposition directly
+a <- cbind(1, x, x^2)
+qr.coef(qr(a), y)
+
+# using least squares
+a <- cbind(x, x^2)
+lsfit(a, y)$coefficients
+
+# using a linear model
+xx <- x*x
+m <- lm(y ~ x + xx)
+coef(m)