# A Gentle Introduction to Linear Regression With Maximum Likelihood Estimation

Last Updated on November 1, 2019

Linear regression is a classical model for predicting a numerical quantity.

The parameters of a linear regression model can be estimated using a least squares procedure or by a maximum likelihood estimation procedure. Maximum likelihood estimation is a probabilistic framework for automatically finding the probability distribution and parameters that best describe the observed data. Supervised learning can be framed as a conditional probability problem, and maximum likelihood estimation can be used to fit the parameters of a model that best summarizes the conditional probability distribution, so-called conditional maximum likelihood estimation.

A linear regression model can be fit under this framework and can be shown to derive an identical solution to a least squares approach.

In this post, you will discover linear regression with maximum likelihood estimation.

After reading this post, you will know:

• Linear regression is a model for predicting a numerical quantity and maximum likelihood estimation is a probabilistic framework for estimating model parameters.
• Coefficients of a linear regression model can be estimated using a negative log-likelihood function from maximum likelihood estimation.
• The negative log-likelihood function can be used to derive the least squares solution to linear regression.

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