In the second scenario we only have one residual, r 4 = 30 r_4 = 30 r 4 = 3 0.This just means that we care more about large residuals than we do about small residuals. Squaring the residuals we magnify the effect large We use the SOSR to measure how well (or rather how poorly) a line fits our data. This can’t be a good thing, can it? Well, in our case it actually is! R 1 r_1 r 1 decreased, while r 2 r_2 r 2 increased 10-fold and r 3 r_3 r 3 increased 40-fold! If we have three residuals r 1 = 0.5 r_1 =0.5 r 1 = 0. We wanted to calculate the sum of residuals,īut if we square each term, then large residuals increase in size a lot more than small residuals! If we compare the SOSR with the SOR, you might say: squaring the residuals yields a different result than the one we actually wanted, doesn’t it? Now we could try and correct our SOSR by taking the square root of every residual.īut the thing is, not “correcting” our SOSR might actually be beneficial. the derivative of x 2 x^2 x 2 is just 2 x 2x 2 x). Ourselves, we avoid using the SOAR and use the SOSR insteadīecause its derivative is very simple (f.e. So in order to make things a bit easier for We will take a look at these two techniques later on in the post. Post, but they are needed for finding the normal equation or performing Since the SOAR tells us how badĪ function performs, we are interested in finding the lowest possible value of it,Īnd therefor we need the derivative of it. ![]() Need to take the derivative of our metric if we want to find it’s minimum, Why do we need the derivative of the SOAR? We
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