can polyfit give R^2 value for linear fit?

[noob]

Hi all,
Sorry I'm asking this question as its own thread:

Can polyfit give R^2 value for linear fit? How??

Thanks a lot.
-Noob

[Tom Lane]

> Can polyfit give R^2 value for linear fit? How??

Noob, it does not compute this directly but you can compute it using the
"normr" field in the output structure. This shows that you get the same
results as from the regstats function in the Statistics Toolbox.

>> load census
>> [p,s] = polyfit(cdate,pop,2);
>> 1 - s.normr^2 / norm(pop-mean(pop))^2
ans =
0.99871296577201
>> regstats(pop, cdate,'quadratic', 'rsquare')
ans =
source: 'regstats'
rsquare: 0.99871296577201

-- Tom

[Ben]

noob <no...@noob.noob> wrote in message <ef25e...@webx.raydaftYaTP>...

From http://www.mathworks.com/help/matlab/ref/polyfit.html:

[p,S] = polyfit(x,y,n) returns the polynomial coefficients p and a structure S for use with polyval to obtain error estimates or predictions. Structure S contains fields R, df, and normr, for the triangular factor from a QR decomposition of the Vandermonde matrix of x, the degrees of freedom, and the norm of the residuals, respectively. If the data y are random, an estimate of the covariance matrix of p is (Rinv*Rinv')*normr^2/df, where Rinv is the inverse of R.

I had this question too, I'm not sure if this is the right way to go about it.

[John D'Errico]

"Ben" wrote in message <loufht$2ol$1...@newscl01ah.mathworks.com>...

You could just use polyfitn, from the file exchange.

It returns R^2, as well as some other parameters.

John

[Ben]

"Ben" wrote in message <loufht$2ol$1...@newscl01ah.mathworks.com>...

Follow-up to earlier answer

If x and y are your data vectors

p = polyfit(x,y,degree);
polydata = polyval(p,x);
sstot = sum((y - mean(y)).^2);
ssres = sum((y - polydata).^2);
rsquared = 1 - (ssres / sstot);