computeCost.m Linear Regression Cost Function - Machine Learning

Key Takeaways

okay so what we're going to try to do in this video is implement the cost function for linear regression which is this formula right here and so it uses the hypothesis which is this formula theta transpose X and this formula is dependent upon the dimensions of theta and X so in our case it might look differently than this formula here so if we move to MATLAB and we go to the compute cost we're first going to do is just check the dimensions of our X and our data we can write X size and our theta size and we can also print our X and our data and so we run this and so here I've actually out commented this part of the code because this is for gradient descent which we haven't implemented yet so if we want just this part which uses our cost function or our compute cost function we see that our excise is of dimensions 97 by 2 and our theta is a 2 by 1 vector so theta transpose X is not going to work in this case so what we want is that our theta 0 here to be multiplicative by our interceptor term X 0 which is just equal to 1 and R theta want to be multiplicative by our X 1 and how we can do that in this case is by taking x times theta and we can see that we can do that because we can take - this is a ninety-seven by two matrix by a two by one so these twos are going to cancel out and we're going to get our hypothesis as a ninety seven by one so if we try to take x times data and set that as our hypothesis and we can also check the size of H which should be a ninety seven by one so that's good and so we seem to have implemented that correctly and so the next step is to take after we've implemented the hypothesis is to take H minus y and you can implement this in a for loop to and and but we're going to doing in a vectorized code in this example so first we have to check that H and Y is of the same dimensions to be able to subtract them so what we can do is check size age size Y and we see that they're both nine 897 by one so that means that we can just take H minus y which is going to take our our first value of H minus our first value of y and the second value of H minus the second value of y and so on and then we're going to take all of this and take it raise to two and notice here that this is a element-wise power so for matlab that's dot raised to and after that we're going to take this sum sum of that which is going to sum that ninety seven by one vector into a one by one and then take that times 1 over 2 times em and then that's going to be our cost cost value so we can clean this up a little bit and then check if ok so seems like we're missing a parenthesis ok and there we see to have get gotten the right values so thank you for watching