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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

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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.

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