Four levels, coded as −3, −1, 1, and 3 were chosen for each of two variables X1 and X2, to provide a total of sixteen experimental conditions when all possible combinations (X1,X2) were taken. It was decided to use the resulting sixteen observations to fit a regression equation including a constant term, all possible first-order, second-order, third-order and fourth-order terms in X1 and X2. The data were fed into a computer routine which ususlly obtains a vector estimate b = (X X) −1X Y The computer refused to obtain the estimates. Why? The experimenter, who had meanwhile examined the data, decided at this stage to ignore the levels of variable X2 and fit a fourth-order model in