I have a homework problem that asks me to fit a one way ANCOVA model to a set of data (which I feel comfortable with). The model is represented as

yij = μi + γzij + eij

where i indicates temperature and j indicates tree.

Then I am asked to replace the temperature effects with a quadratic polynomial:

yij = Β0 + Β1Ti + Β2Ti2 + γzij + eij

This is where things get confusing for me. Conceptually I don't understand what is going on so I'm hoping that someone can explain it to me a little better than the one line in my textbook. Thanks!

Also this is an excerpt about the data being used in this problem with a portion of the table:

Data Description

Portion of Data Table


1 Answer 1


When you replace the temperature effects with the quadratic polynomial, you're effectively changing temperature from a factor to a numeric variable. With that change, you are going from analyzing an ANCOVA (where you have both a factor and a regression variable) to a pure regression model (three regression variables). This change will alter your Sum of Squares values, MSE values, and make your degrees of freedom for temperature go from 4 (ie, 5-1) in the ANCOVA to 1 for temp (which is your B1Ti) and 1 for the temp^2 (which is your B2Ti^2) in the polynomial model. Your covariate will stay the same in both, as you are not changing it from one equation to the next. Hope this helps.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.