Next: Fitting Examples for linear regression, Previous: Large Linear Systems, Up: Least-Squares Fitting [Index]

When using models based on polynomials, care should be taken when constructing the design matrix
*X*. If the *x* values are large, then the matrix *X* could be ill-conditioned
since its columns are powers of *x*, leading to unstable least-squares solutions.
In this case it can often help to center and scale the *x* values using the mean and standard deviation:

x' = (x - mu)/sigma

and then construct the *X* matrix using the transformed values *x'*.