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st: Interpretation of quadratic terms

From   Rosie Chen <>
Subject   st: Interpretation of quadratic terms
Date   Mon, 8 Mar 2010 10:28:29 -0800 (PST)

Dear all,

    I have a question regarding how to interpret quadratic terms in regression, and would appreciate your help very much. 

    Because the non-linear nature of the relationship between X and Y; I need to include quadratic terms in the model. To avoid multicollinearity problem with the original variable and its quadratic term, I centered the variable first (X) and then created the square term (Xsq). The model with the quadratic term (Xsq) was proved to be significantly better. Suppose the output is like the following (both coefficients are significant), how to interpret the results? The two signs are opposite. Could anyone provide some insight? Thank you very much in advance!  --Rosie

y= a + 1.3*X - 0.2*Xsq + e

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