matlab - Computing Cost function for Linear regression with one variable without using Matrix -

i'm new matlab , machine learning , tried compute cost function gradient descent.

the function computecost takes 3 arguments:

• x mx2 matrix
• y m-dimensional vector
• theta : 2-dimensional vector

i have solution using matrix multiplication

function j = computecost(x, y, theta)   m = length(y);   h = x * theta;   serror = (h - y) .^ 2;   j = sum(serror) / (2 * m); end 

but now, tried same without matrix multiplication

function j = computecost(x, y, theta)   m = length(y);   s = 0;   = 1:m     h = x(i, 1) + theta(2) * x(i, 2);     s = s + ((h - y(i)) ^ 2);   end   j = (1/2*m) * s; end 

but didn't same result, , first sure (i use before).

you have 2 slight (but fundamental) errors - pretty simple errors though can overlooked.

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1. you forgot include bias term in hypothesis:

   h = x(i,1)*theta(1) + x(i,2)*theta(2); %//         ^^^^^^ 

   remember, hypothesis when comes linear regression equal theta^{t}*x. didn't include of theta terms - second term.

2. your last statement normalize (2*m) off. have as:

   j = (1/2*m) * s; 

   because multiplication , division have same rules of operation, same (1/2)*m , that's not want. make sure (2*m) has brackets surrounding ensure evaluated s / (2*m):

   j = (1/(2*m)) * s; 

   this ensure 2*m evaluated first, reciprocal of taken multiplication of sum of squared errors.

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when fix problems, same results using matrix formulation.

btw, slight typo in code. should m = length(y), not m = length(y).