Exercise 1.1 Write the following models in matrix notation: (a) Multiple regression yi =0+1xi1+2xi2+3xi3+ei, i = 1,

Exercise 1.1 Write the following models in matrix notation:

(a) Multiple regression yi =β0+β1xi1+β2xi2+β3xi3+ei,

i = 1, . . . , 6.

(b) Two-way ANOVA with interaction yi jk = μ +αi+β j +γi j +ei jk, i = 1,2, 3, j = 1, 2, k = 1, 2.

(c) Two-way analysis of covariance (ACOVA) with no interaction yi jk = μ +αi+β j +γ xi jk +ei jk, i = 1,2, 3, j = 1, 2, k = 1, 2.

(d) Multiple polynomial regression yi =β00+β10xi1+β01xi2+β20x2 i1+β02x2 i2+β11xi1xi2+ei, i = 1, . . . , 6.