I am taking the course on Machine Learning and unable to grasp the concept of MLE for linear regression. Can anyone give some numerical example ? Most of the content I read on internet was theoretical.

Following is my understanding : For estimating MLE I will need input variable vectors (say X ), Output variables (Y), and σ². If Model is Y = (A1) + (A2)X + e, then I have to maximize P(Y|X,σ²) and find out value for A1 and A2 is this correct?


  • $\begingroup$ Yes, this how the mle works in general. You form the joint distribution of your observed sample, which is called the likelihood, and you find the parameters that maximize it. Then these parameters have optimal properties, under the regularity conditions. In the linear model, other than the slope and intercept parameters, you also have to find an estimate for $\sigma^2$, assuming it is unknown. $\endgroup$
    – JohnK
    Sep 20, 2015 at 9:01
  • $\begingroup$ I see there are a couple of votes to close the question for it being a self-study question. If it indeed is a self-study question, please add the relevant self-study tag and read its Wiki. $\endgroup$ Sep 20, 2015 at 11:43