# OLS¶

OLS is an abbreviation for ordinary least squares.

The class estimates a multi-variate regression model and provides a variety of fit-statistics. To see the class in action download the ols.py file and run it (python ols.py). This )# will estimate a multi-variate regression using simulated data and provide output. It will also provide output from R to validate the results if you have rpy installed (http://rpy.sourceforge.net/).

To import the class:

In [ ]:
#!python
import ols


After importing the class you can estimate a model by passing data to it as follows

In [ ]:
#!python
mymodel = ols.ols(y,x,y_varnm,x_varnm)


where y is an array with data for the dependent variable, x contains the independent variables, y_varnm, is a string with the variable label for the dependent variable, and x_varnm is a list of variable labels for the independent variables. Note: An intercept term and variable label is automatically added to the model.

## Example Usage¶

In [ ]:
#!python
>>> import ols
>>> from numpy.random import randn
>>> data = randn(100,5)
>>> y = data[:,0]
>>> x = data[:,1:]
>>> mymodel = ols.ols(y,x,'y',['x1','x2','x3','x4'])
>>> mymodel.p               # return coefficient p-values
array([ 0.31883448,  0.7450663 ,  0.95372471,  0.97437927,  0.09993078])
>>> mymodel.summary()       # print results
==============================================================================
Dependent Variable: y
Method: Least Squares
Date: Thu, 28 Feb 2008
Time: 22:32:24
# obs:             100
# variables:         5
==============================================================================
variable     coefficient     std. Error      t-statistic     prob.
==============================================================================
const           0.107348      0.107121      1.002113      0.318834
x1             -0.037116      0.113819     -0.326100      0.745066
x2              0.006657      0.114407      0.058183      0.953725
x3              0.003617      0.112318      0.032201      0.974379
x4              0.186022      0.111967      1.661396      0.099931
==============================================================================
Models stats                         Residual stats
==============================================================================
R-squared             0.033047         Durbin-Watson stat   2.012949
Adjusted R-squared   -0.007667         Omnibus stat         5.664393
F-statistic           0.811684         Prob(Omnibus stat)   0.058883
Prob (F-statistic)    0.520770            JB stat              6.109005
Log likelihood       -145.182795       Prob(JB)             0.047146
AIC criterion         3.003656         Skew                 0.327103
BIC criterion         3.133914         Kurtosis             4.018910
==============================================================================


== Note ==

Library function [http://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.lstsq.html numpy.linalg.lstsq()] performs basic OLS estimation.

Section author: VincentNijs, Unknown[103], DavidLinke, AlanLue

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