10.14. Relationship between analysis of variance and regression. Any analysis of variance model can be expressed in terms of the general linear model y $ x& % (, where the X matrix consists of 0s and 1s. Show that the single-factor model yij $ $ % .i % 'ij , i $ 1, 2, 3, j $ 1, 2, 3, 4 can be written in general linear model form. Then,

(a) Write the normal equations (X6X) $ X6y and compare them with the normal equations found for this model in Chapter 3.

(b) Find the rank of X6X. Can (X6X)!1 be obtained?

(c) Suppose the first normal equation is deleted and the restriction is added. Can the resulting system of equations be solved? If so, find the solution. Find the regression sum of squares X6y, and compare it to the treatment sum of squares in the single-factor model.