OLS Regression: Scikit vs. Statsmodels?

If you use statsmodels, I would highly recommend using the statsmodels formula interface instead. You will get the same old result from OLS using the statsmodels formula interface as you would from sklearn.linear_model.LinearRegression, or R, or SAS, or Excel.

smod = smf.ols(formula ='y~ x', data=df)
result = smod.fit()
print(result.summary())

When in doubt, please

1. try reading the source code
2. try a different language for benchmark, or
3. try OLS from scratch, which is basic linear algebra.

It sounds like you are not feeding the same matrix of regressors X to both procedures (but see below). Here's an example to show you which options you need to use for sklearn and statsmodels to produce identical results.

import numpy as np
import statsmodels.api as sm
from sklearn.linear_model import LinearRegression

# Generate artificial data (2 regressors + constant)
nobs = 100 
X = np.random.random((nobs, 2)) 
X = sm.add_constant(X)
beta = [1, .1, .5] 
e = np.random.random(nobs)
y = np.dot(X, beta) + e 

# Fit regression model
sm.OLS(y, X).fit().params
>> array([ 1.4507724 ,  0.08612654,  0.60129898])

LinearRegression(fit_intercept=False).fit(X, y).coef_
>> array([ 1.4507724 ,  0.08612654,  0.60129898])

As a commenter suggested, even if you are giving both programs the same X, X may not have full column rank, and they sm/sk could be taking (different) actions under-the-hood to make the OLS computation go through (i.e. dropping different columns).

I recommend you use pandas and patsy to take care of this:

import pandas as pd
from patsy import dmatrices

dat = pd.read_csv('wow.csv')
y, X = dmatrices('levels ~ week + character + guild', data=dat)

Or, alternatively, the statsmodels formula interface:

import statsmodels.formula.api as smf
dat = pd.read_csv('wow.csv')
mod = smf.ols('levels ~ week + character + guild', data=dat).fit()

Edit: This example might be useful: http://statsmodels.sourceforge.net/devel/example_formulas.html