title: Statsmodels OLS Regression: Log-likelihood, uses and interpretation
body: <p>I'm using python's statsmodels package to do linear regressions. Among the output of <code>R^2</code>, <code>p</code>, etc there is also "log-likelihood". In the docs this is described as "The value of the likelihood function of the fitted model." I've taken a look at the source code and don't really understand what it's doing.</p>
  
  <p>Reading more about likelihood functions, I still have very fuzzy ideas of what this 'log-likelihood' value might mean or be used for. So a few questions:</p>
  
  <ul>
  <li><p>Isn't the value of likelihood function, in the case of linear regression, the same as the value of the parameter (<code>beta</code> in this case)? It seems that way according to the following derivation leading to equation 12: <a href="http://www.le.ac.uk/users/dsgp1/COURSES/MATHSTAT/13mlreg.pdf" rel="nofollow">http://www.le.ac.uk/users/dsgp1/COURSES/MATHSTAT/13mlreg.pdf</a></p></li>
  <li><p>What's the use of knowing the value of the likelihood function? Is it to compare with other regression models with the same response and a different predictor? How do practical statisticians and scientists use the log-likelihood value spit out by statsmodels?</p></li>
  </ul>