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, 201015 yr by dttom

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.