Exercise 8.2 In the 4×4 Latin square of the examples, show that the 9 degrees of freedom for (αβ ) interaction are being divided into 3 degrees of freedom for γ

and 6 degrees of freedom for error.

the model yhi jk = μ +αh+βi+γ j +ηk +ehi jk.
C1 C2 C3 C4 C5 R1 T1τ1 T2τ3 T3τ5 T4τ2 T5τ4 R2 T2τ2 T3τ4 T4τ1 T5τ3 T1τ5 R3 T3τ3 T4τ5 T5τ2 T1τ4 T2τ1 R4 T4τ4 T5τ1 T1τ3 T2τ5 T3τ2 R5 T5τ5 T1τ2 T2τ4 T3τ1 T4τ3 Extend the analysis to an arbitrary a×a Graeco-Latin square.