# Machine Learning Ex2 – Linear Regression

March 22, 2011
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(This article was first published on YGC » R, and kindly contributed to R-bloggers)

Thanks to this post, I found OpenClassroom. In addition, thanks to Andrew Ng and his lectures, I took my first course in machine learning. These videos are quite easy to follow. Exercise 2 requires implementing gradient descent algorithm to model data with linear regression.

?View Code RSPLUS
 ```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 ``` ```gradDescent <- function(x, y, alpha=0.07, niter=1500, eps=1e-9) { x <- cbind(rep(1, length(x)), x) theta.old <- rep(0, ncol(x)) m <- length(y) for (i in 1:niter) { theta <- gradDescent_internal(theta.old, x, y, m) if (all(abs(theta - theta.old) <= eps)) { break } else { theta.old <- theta } } return(theta) }   gradDescent_internal <- function(theta, x, y, m) { h <- sapply(1:nrow(x), function(i) theta %*% x[i,]) j <- (h-y) %*% x grad <- 1/m * j theta <- theta - alpha * grad return(theta) }   require(ggplot2) x <- read.table("ex2x.dat", header=F) y <- read.table("ex2y.dat", header=F) x <- x[,1] y <- y[,1] p <- ggplot() + aes(x, y) + geom_point() + xlab("Age in years") + ylab("Height in meters")   theta <- gradDescent(x,y)   yy <- theta[1] + theta[-1] %*% t(x) yy <- as.vector(yy) predicted <- data.frame(x=x, y=yy) p+geom_line(data=predicted, aes(x=x,y=y))```

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