4.7. Analysis of Covariance

When we want to compare various treatments, but the responses are affected by not only the particular treatments but also by certain other variables termed covariates or concomitant variables, we need to modify the analysis to account for these covariates and eliminate their effects. In other words, to make a fair comparison of various treatments, the data on the response variables need to be made comparable by first adjusting for the covariates. These situations commonly occur in social, biological, medical, physical, and other sciences.

For analyzing these data we utilize the following model

where the matrices ...

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