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# RE: st: RE: Interpretation of quadratic terms

 From "Nick Cox" To Subject RE: st: RE: Interpretation of quadratic terms Date Tue, 9 Mar 2010 12:19:36 -0000

```Looking at residuals too is a good idea, but what I had in mind was just
plotting the predicted. Here's a dopey example (in this case the
quadratic is not a good idea, but the example is just to show
technique).

sysuse auto
gen weight2 = weight^2
logit foreign weight weight2

predict predict
scatter foreign weight || mspline predict weight, bands(200)

The last two commands could be replaced by

regplot

gen weight2 = weight^2
logit foreign weight weight2

The second and third commands, repeated just above, could be combined in
Stata 11 using factor variable notation.

logit foreign weight c.weight#c.weight

OR

logit foreign c.weight##c.weight

Nick
n.j.cox@durham.ac.uk

Rosie Chen

Nick, thank you for the guidance. The model I am estimating is a
logistic regression. What I did to check the plot was to save the
residual of the model, and then plotted the standardized residual
against the predictor. I didn't really found a curve-linear
relationship.

Is there anything wrong with the way I plot the residual? If not, then
why the inclusion of a quadratic term actually improves the model
fitting when I made a model comparison using the -2log-likelihood? In
addition, the nonsignificant predictor in the original form turned to be
appreciated.

Nick Cox <n.j.cox@durham.ac.uk>

I don't know what kind of guidance you need, but the first step is
surely to plot this curve and think about its substantive interpretation
within the entire range of the data. That should include bringing in
whatever science is behind this analysis.

Rosie Chen
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.

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

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```