Alternate Coding Schemes for the Regression Approach to Analysis of Variance. Consider Eq. (8.18), which represents the regression model corresponding to an analysis of variance with three treatments and $n$ observations per treatment. Suppose that the indicator variables $x_{1}$ and $x_{2}$ are defined as

Eq.(8.18)

a. Show that the relationship between the parameters in the regression and analysis-of-variance models is

b. Write down the $\mathbf{y}$ vector and $\mathbf{X}$ matrix.

c. Develop an appropriate sum of squares for testing the hypothesis $H_{0}: \tau_{1}=\tau_{2}=\tau_{3}=0$. Is this the usual treatment sum of squares in the oneway analysis of variance?

Transcribed Image Text:

Yij Bo+B1x1; +2x2j+Ej, i=1, 2, 3, j=1, 2,...,n