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Linear regression in Octave
% scaled features.
% x = square feet
% y = sale price
x = [1, 2, 4];
y = [2, 2.5, 3];
% function to calculate the predicted value
function result = h(x, t0, t1)
result = t0 + t1 * x;
end
% 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.
function distance = cost(theta_0, theta_1, x, y)
distance = 0;
for i = 1:length(x) % arrays in octave 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);
end
% get how far off we were on average
distance = distance / length(x);
end
alpha = 0.1;
iters = 1500;
m = length(x);
% initial values
theta_0 = 0;
theta_1 = 0;
for i = 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 = 1:m
cost_0 += (h(x(j), theta_0, theta_1) - y(j));
end
temp_0 = theta_0 - alpha * 1/m * cost_0;
cost_1 = 0;
for j = 1:m
cost_1 += ((h(x(j), theta_0, theta_1) - y(j)) * x(j));
end
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
disp([theta_0, theta_1, cost(theta_0, theta_1, x, y)]);
end
% scale the values of theta, they
% were too small because we did feature scaling
theta_0 = theta_0 * 100000;
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 *= 1000;
y *= 100000;
% plot the data and the best-fit line
figure;
set (0,'defaultaxesposition', [0.15, 0.1, 0.7, 0.7]);
plot(x, y, 'rx');
hold on;
plot(1000:4000, h(1000:4000, theta_0, theta_1));
% tell me how much to sell a 3000 square foot home for:
disp(h(3000, theta_0, theta_1));
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