ABSTRACT
There are many experimental situations where more than one covariate is measured on each experimental unit. For data collected from a one-way treatment structure in a completely randomized design structure with k covariates, a model for each treatment can be expressed as
(4.1)
where x
denotes the value of the p
covariate on the ij
experimental unit,
α
denotes the intercept of the i
treatment’s regression surface,
β
denotes the slope in the direction of the p
covariate for treatment i, and it is assumed that
ε
, j = 1,
y X X X
= + + +…+ +
= … = …
α β β β ε1 2 2 1 2 1 2, , , , , , ,
the data for each treatment. Thus, each treatment’s model is a multiple linear regression model. The usual regression diagnostics should be applied to each treatment’s data to check for model adequacy. The treatment variances should be tested for equality. When there is only one covariate, the analysis of covariance consists of comparing several regression lines. In the multiple covariates case, the analysis of covariance consists of comparing several regression planes or hyper-planes.
