Date:         Sat, 10 May 2003 21:20:26 +1000
Reply-To:     doug <queanbeyan@HOTMAIL.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         doug <queanbeyan@HOTMAIL.COM>
Organization: Global Crossing Internet
Subject:      Re: how to calculate linear regression by hand?

Michael,

You can use excel to do the transposes for matrices to get the (XtX)-1XtY
vector outcome that will contain the beta values.  Otherwise, if you data
are not too numerous you could do the inverses, transposes and
multiplications by hand.

The (xtx)-1Xty method works every time and I owe much of my understanding
(or lack thereof) to my stats lecturer who insisted that I learn the manual
method!!

Basically if you have your X values (for simple linear regression it is
dead-set simple) and you are including an intercept, make a matrix of nx2
form where n= number of obs (lets say you have 2 values of x and y).  Make
the first column all equal to 1 and populate the second column with the x
values.  Then create a vector (nx1 matrix) with the y values.

First step is to transpose of the x matrix (2x2),
second multiply this by the original x matrix.
third take the inverse of this and multiply this by transposed x matrix from
step 1
finally, multiply this by the y vector and hey presto you have your OLS beta
values.

I can send you an excel spreadsheet that will do the matrix multiplications,
transpositions and inverses if you wish.

Hope this helps.

Doug


"Yu, Michael" <michael.yu@SPCORP.COM> wrote in message
news:51E9450E2DA1D4118DB400508BF9AC34092B6B85@kenmsg32.schp.com...
> off topic: What's the formula to compute linear regression by hand?
>
> eg, 10 pairs of x and y
> ( x1, y1 )
> ( x2, y2 )
> ...
> ( x10, y10 )
>
> there's a formula to get a least square fit
> y= a x + b
>
> where can I find such a formula so I can compute it myself to check
against
> the output from SAS?
>
> Thanks,
>
> Hsiwei
>
>
>
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