Alternate Coding Schemes for tbe 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 x1 and x2 are defi ned as x1 1 1

= −1 if observation is from treatment if observation is from treatment otherwise 2

0

⎧

⎨

⎪

⎩

⎪

x2 1 2

= −1 if observation is from treatment if observation is from treatment otherwise 3

0

⎧

⎨

⎪

⎩

⎪

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

b. Write down the y vector and X matrix.

c. Develop an appropriate sum of squares for testing the hypothesis H0 : τ1 = τ2 = τ3 = 0. Is this the usual treatment sum of squares in the one -
way analysis of variance?

B = 1+2+3 3. B B-