Back to library index.

Package regress (in regress.i) -

Index of documented functions or symbols:

DOCUMENT model = regress(y, [x1,x2,x3,...]) or model = regress(y, [x1,x2,x3,...], axes, vals, chi2) Performs linear regression analysis, that is, a linear least squares fit of the parametric model y = model(1)*x1 + model(2)*x2 + model(3)*x3 + ... = model(+) * [x1,x2,x3,...](..,+) to the supplied data Y, [X1,X2,X3,...]. Y is an array, and the Xi arrays should have the same dimensions as Y, or more accurately [X1,X2,X3,...] must have one trailing dimension beyond the dimensions of Y; the length of the trailing dimension is the number of parameters in the model. Use the sigy= keyword to pass in the standard deviations of the Y values; sigy must be conformable with Y. The returned model has minimum chi2, where chi2 = sum( (y - model(+) * [x1,x2,x3,...](..,+))^2 / sigy^2 ) The default sigy=1, that is, all points have equal weight in chi2. The optional AXES, VALS, and CHI2 arguments are outputs. AXES are the axes of the error ellipsoid of the fitted parameters, and VALS are the corresponding singular values. AXES(i,) is the vector in the space of model() corresponding to VALS(i). The VALS are non-negative and arranged in descending order. CHI2 is the chi2 value for the returned model, divided by the number of degrees of freedom in the fit, numberof(y)-sum(vals>rcond*vals(1)). AXES(i,) are mutually orthogonal unit vectors; you should arrange the magnitudes of X and Y so this makes sense - their scale factors may matter. Usually this means arranging that the magnitudes of the elements of the returned model not differ too wildly. Often and unexpectedly, the data do not permit a definitive choice of the model(); there may be entire subspaces of the model space which produce indistinguishably good fits to the data. The signature of this problem is that some of the VALS may be zero or very small. The rcond= keyword permits you to specify how small a singular value, relative to the largest, VALS(1), you are willing to consider. The AXES(i,) corresponding to VALS(i) smaller than rcond*VALS(1) will be given zero contribution to the returned model(). The default value is rcond=1.e-9. If any of the returned VALS is less than rcond*VALS(1) you should either change the scales of Y or some X, or remove some of the X (the ones which aren't contributing) to eliminate the problem. The regress function reverses the sign of any VALS which are less than rcond*VALS(1), so you can quickly identify them. Examples: ab = regress(y, [1,x]); ab(1)+ab(2)*x is best fit line to y(x) ab = regress(y, [1,x,x^2,x^3]); poly(x,ab(1),ab(2),ab(3)) is best fit cubic to y(x) ab = regress(y, [cos(x),sin(x)]); ab(1)*cos(x)+ab(2)*sin(x) is best fit period 2*pi sine wave to y(x)

SEE ALSO: regress_cov

DOCUMENT cov = regress_cov(axes, vals) or cov = chi2 * regress_cov(axes, vals) Return the covariance matrix for the model returned by regress, where AXES and VALS are the values returned by regress. This is a symmetric matrix representing covariance(model(i),model(j)) that is, the variances (on the diagonal i=j) and correlations of the model parameters. If you did not specify the sigy= keyword in the original call to regress, then the absolute magnitudes of the covariance matrix elements do not mean much. In case you wish to use the quality of the fit itself as an estimate of the errors sigy in the original Y values, assuming they are all equal, you can multiply by the CHI2 returned by regress, as in the second form above, in order to produce an estimated error in the fit. See Numerical Recipes for caveats, but this is what commercial statistics software generally does. cov(1::numberof(vals)+1) are the variances of the model parameters themselves.

SEE ALSO: regress