# [SciPy-user] linear regression

ms devicerandom@gmail....
Wed May 27 14:00:25 CDT 2009

```josef.pktd@gmail.com ha scritto:
> On Wed, May 27, 2009 at 12:35 PM, ms <devicerandom@gmail.com> wrote:
>> josef.pktd@gmail.com ha scritto:
>>>> Have a look here <http://www.scipy.org/Cookbook/LinearRegression>
>>> y = Beta0 + Beta1 * x + Beta2 * x**2   is the second order polynomial.
>>>
>>> I also should have looked, polyfit returns the polynomial coefficients
>>> but doesn't calculate the variance-covariance matrix or standard
>>> errors of the OLS estimate.
>> AFAIK, the ODR fitting routines return all these parameters, so one can
>> maybe use that for linear fitting too.
>
> you mean scipy.odr?

Yes.
I use it for non-linear fitting, and it gives parameters, standard
deviations and covariance matrix.

> I never looked at it in details. Conceptionally it is very similar to
> standard regression, but I've never seen an application for it, nor do
> I know the probability theoretic or econometric background of it. The
> results for many cases will be relatively close to standard least
> squares.

You can explicitly tell the odr function to use least squares fitting.

> A google search shows links to curve fitting but not to any
> econometric theory.

The math of fitting data to a function, as far as I know, is independent
of the field of application. The functions and the data, of course, are
not. :)

> The difference between curve fitting and (maybe prediction) and
> parameter estimation in many social/economic sciences is that we want
> to get a reliable parameter estimate and not just a well fitting
> curve.

Ehm, I don't know what is your knowledge of sciences, but trust me, no
one does curve fitting only to obtain "a well fitting curve": everyone
wants parameters, obviously, and their statistics.
scipy.odr gives me these nicely.

> How much does the average lifetime income increase when finishing
> college compared to only finishing high school? Did the price of oil
> go up because of demand side or supply side effects? Did the
> availability of contraceptives decrease crime?

On a side note, you won't answer these interesting questions with linear
fitting only, because correlation does not mean causation.

m.
```