Models lacking intercept

If the true model contains quadratic terms then the estimate of the intercept, Pq, of the first-order model will be biased. The lack-of-fit of the first-order model due to quadratic effects can be tested by adding center points to the design. 

The lack-of-fit error is slightly smaller titan the replicate error, in all cases except when the intercept is removed from die model for the dataset B, where it is large, 10.693. This suggests that adding the intercept term to the second dataset makes a big difference to the quality of the model and so die intercept is significant. 

The vector, y, is a column vector of spectroscopic data for each sample at one wavelength. The matrix X contains the concentrations of the samples. If an intercept is included in the model, then the first column of X must be a column of Is. The vector e is a column of residuals associated with lack of fit in the model. The vector e contains the errors that are minimized in the regression analysis. 

---