单变量线性回归的预测方程、代价函数与梯度下降

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此代码是未进行向量化的

代价函数 

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function J = computeCost(X, y, theta)
m = length(y); % number of training examples
J = 0;
for i=1:m
J += (theta(1)+ theta(2)*X(i,2)-y(i))^2;
end
J = J/(2*m);
end

梯度下降 

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function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
m = length(y);
J_history = zeros(num_iters, 1);
for iter = 1:num_iters
k = 0;
o = 0;
for i=1:m
  k +=(theta(1)+ theta(2).*X(i,2)-y(i));
  o +=(theta(1)+ theta(2).*X(i,2)-y(i)).*X(i,2);
end
    theta(1) -= (alpha/m).* k;
    theta(2) -= (alpha/m).* o;
    J_history(iter) = computeCost(X, y, theta);
end
end

运行结果

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