dttom Posted September 15, 2010 Share Posted September 15, 2010 (edited) I am not sure if I call the topic 'linear regression' is right, actually it is about 'least square analysis' in constructing a best-fit line, but when I googles the phase 'linear regression' some relevant information pops out. So assuming now we have a set of data, y values correspond to x values; plotting it in y vs. x manner it appears to form a straight line, but now we want the best-fit line. The method is to select an m value and a c value, by y = mx + c, to minimize di = sum[(actual y)-(computed y)]^2, I can do this step. What I got difficulty is to find the standard deviation of m and c. Sy^2 = di/(n-2); In a lecture I heard about: Sm^2 = (Sy^2)(n/D) where n is the observation size and D = nsum(Xi^2)-(sum(Xi))^2 and; Sc^2 = (Sy^2)(sum(Xi^2)) I do not know how these equations are derived. There is no explanation in the lecture as it simply uses them in applications, while I am interested in the derive-process. I googled it and some suggested Sm^2 = (Sy^2)(sum(dm/dyi)) ===partial differentiation, similar formula is for Sc^2 by replacing dm/dyi with dc/dyi. Again I do not know how they are derived. Could somebody help? Edited September 15, 2010 by dttom Link to comment Share on other sites More sharing options...
ewmon Posted September 17, 2010 Share Posted September 17, 2010 The LSM (Least Squares Method) is a form of linear regression. minimize di = sum[(actual y)-(computed y)]^2 I think this should say: minimize di = sum{[(actual y)-(computed y)]^2} I've studied the LSM, and I don't recall a standard deviation of m or c. Link to comment Share on other sites More sharing options...
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