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st: RE: Interpretation of quadratic terms
From
Rodolphe Desbordes <[email protected]>
To
"'[email protected]'" <[email protected]>
Subject
st: RE: Interpretation of quadratic terms
Date
Mon, 8 Mar 2010 18:42:31 +0000
Dear Rosie,
If the coefficient on X is positive and the coefficient on X^2 is negative, that suggests that X has a positive effect on Y until a turning point is reached, e.g. 1.3/(2*0.2)=3.25. Beyond that value, X has a negative impact on Y.
Rodolphe
PS: I am not sure that `centering' reduces multicollinearity.
-----Original Message-----
From: [email protected] [mailto:[email protected]] On Behalf Of Rosie Chen
Sent: lundi 8 mars 2010 18:28
To: [email protected]
Subject: st: Interpretation of quadratic terms
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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