linear_regression.R

# scaled features.
# x = square feet
# y = sale price
x <- c(1, 2, 4)
y <- c(2, 2.5, 3)

# function to calculate the predicted value
h <- function(x, t0, t1)
{
    result = t0 + t1 * x
    result
}


# given a theta_0 and theta_1, this function calculates
# their cost. We don't need this function, strictly speaking...
# but it is nice to print out the costs as gradient descent iterates.
# We should see the cost go down every time the values of theta get updated.
cost <- function (theta_0, theta_1, x, y) 
{
    distance <- 0
    for (i in 1:length(x)) # arrays in R are indexed starting at 1
    {
        square_feet <- x[i]
        predicted_value <- theta_0 + theta_1 * square_feet
        actual_value <- y[i]
        # how far off was the predicted value (make sure you get the absolute value)?
        distance <- distance + abs(actual_value - predicted_value)
    }
    # get how far off we were on average
    distance <- distance / length(x)
    distance
}

alpha <- 0.1
iters <- 1500
m <- length(x)

# initial values
theta_0 <- 0
theta_1 <- 0

for (i in 1:iters)
{
    # we store this calculation in temporary variables,
    # because theta_0 and theta_1 must be updated *together*.
    # i.e. we can't update theta_0 and use the new theta_0 value
    # while updating theta_1.
    cost_0 <- 0
    for (j in 1:m)
    {
        cost_0 <- cost_0 + (h(x[j], theta_0, theta_1) - y[j])
    }
    temp_0 <- theta_0 - alpha * 1/m * cost_0
    
    cost_1 <- 0
    for (j in 1:m)
    {
        cost_1 = cost_1 + ((h(x[j], theta_0, theta_1) - y[j]) * x[j])
    }
    
    temp_1 <- theta_1 - alpha * 1/m * cost_1
    
    theta_0 <- temp_0
    theta_1 <- temp_1
    
    # print out the new values of theta for each iteration,
    # as well as the new, lower cost
    print(theta_0, theta_1, cost(theta_0, theta_1, x, y))
    
}

# scale the values of theta, they
# were too small because we did feature scaling
theta_0 <- theta_0 * 100000
theta_1 <- theta_1 * 100

# un-scale the features. So now we should be
# back to [1000, 2000, 4000] for square feet,
# from [1, 2, 4].
x <- x * 1000
y <- y * 100000

plot(x, y, col='red')
lines(1000:4000, h(1000:4000, theta_0, theta_1), col='green')

print(h(3000, theta_0, theta_1))