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# Re: st: interprating orthogonal polynomial regression

 From jl591164@albany.edu To statalist@hsphsun2.harvard.edu Subject Re: st: interprating orthogonal polynomial regression Date Mon, 26 Jul 2010 12:54:38 -0400 (EDT)

```I used the syntax that Maarten provided to translate the coefficients of
the orthogonal polynomials into the original metric of time. The results
are below. Then i guess the equation of the cubic mode is represented in
the row of deg3, that y=.67-1.46t+.42t²-.03t³. Then what is the formula to
get the two reflection points of the curve(the sample mean trajectory
showed that there are two reflection points, and it changes directions
twice)? Thanks a lot.

|      deg1       deg2       deg3      _cons
-------------+--------------------------------------------
deg1 | -.1405198          0          0   .5339751
deg2 |  .5560661  -.0491674          0  -.6281949
deg3 | -1.458612   .4243002  -.0270891   .6659666
_cons |         0          0          0  -.5578475

> *--------------- begin example ----------------
> sysuse auto, clear
> orthpoly weight, deg(3) generate(pw*)
> logit foreign mpg pw1-pw3 rep78
> orthpoly weight, deg(3) poly(P)
> matrix b = e(b)
> // extract the polynomials and the constant
> matrix b = b[1, "foreign:pw1".."foreign:pw3"], b[1,"foreign:_cons"]
> matrix b = b*P
> matlist b
>
> // check
> gen w1 = weight
> gen w2 = weight^2
> gen w3 = weight^3
>
> logit foreign mpg w1-w3 rep78
> *---------------- end example -----------------------
>

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