Correct and incorrect use of multilinear regression

Multilinear regression is applied when experimenters wish to investigate the relationship between a block of predictor variables (X), whose values are fixed by the experimenter, and one or more responses (Y), measured at each experiment. The objective is to find a mathematical equation relating X and Y, by means of regression coefficients. Regression analysis is said to give good results when a squared multiple regression coefficient R2 close to 1 is obtained and when the sum of squares of residuals (differences between experimental value of the response and computed value) is small. However, it must be noted that a bad choice of the experiments renders the obtained regression equation meaningless. In this paper an example of correct and incorrect use of multilinear regression is presented in detail the quality of the coefficients and the goodness of the prediction depend on the experimental design, and the value of R2 gives no information at all about them. A set of criteria useful to judge the quality of an experimental plan, before carrying out any experiment, is proposed.