# Using Maximum Likelihood function to find near-optimal solution

For the context, I was writing my BSc thesis on the topic of Linear Regression through the Origin (RTO). My goal is to analyze RTO, and find the appropriate use cases for it. In the case of simple linear regression, we know that we can take partial derivatives of log-likelihood function $$l$$ to get the maximum likelihood estimators for the slop term, intercept term, and variance. What if we use log-likelihood graph, and since it is convex, take sufficiently small neighborhood around the point that maximizes it, such that the intercept term is zero?

We then can compare obtained model with the model where we force our regression line to go through the origin.

• This will not be better than forcing the linear regression through the origin, since when we force the line through the origin, and then take MLE of it, it will be better in terms of SSE, with given constraint that intercept is zero Nov 13, 2023 at 15:44
• What would be the point of your proposal, when there is an extremely simple formula for the solution?
– whuber
Nov 13, 2023 at 16:49