Module-4-Example-7.R

# https://www.r-bloggers.com/linear-regression-by-gradient-descent/

# generate random data in which y is a noisy function of x
x <- runif(1000, -5, 5)
y <- x + rnorm(1000) + 3

# Look at the scotterplot 
plot(y, x)

# fit a linear model
res <- lm( y ~ x )
print(res)

# plot the data and the model
plot(x,y, col=rgb(0.2,0.4,0.6,0.4), main='Linear Regression ')
abline(res, col='blue')


# squared error cost function
cost <- function(X, y, theta) {
  sum( (X %*% theta - y)^2 ) / (2*length(y))
}

# learning rate and iteration limit
alpha <- 0.01
num_iters <- 1000

# keep history
cost_history <- double(num_iters)
theta_history <- list(num_iters)

# initialize coefficients
theta <- matrix(c(0,0), nrow=2)

# add a column of 1's for the intercept coefficient
X <- cbind(1, matrix(x))


# gradient descent
for (i in 1:num_iters) {
  error <- (X %*% theta - y)
  delta <- t(X) %*% error / length(y)
  theta <- theta - alpha * delta
  cost_history[i] <- cost(X, y, theta)
  theta_history[[i]] <- theta
}

print(theta)

# plot data and converging fit
plot(x,y, col=rgb(0.2,0.4,0.6,0.4), main='Linear regression by gradient descent')
for (i in c(1,3,6,10,14,seq(20,num_iters,by=10))) {
  abline(coef=theta_history[[i]], col=rgb(0.8,0,0,0.3))
}
abline(coef=theta, col='blue')

plot(cost_history, type='line', col='blue', lwd=2, main='Cost function', ylab='cost', xlab='Iterations')