Maximum likelihood estimation

Maximum likelihood estimation (MLE) is a popular model that's used for estimating the parameters of linear regression. MLE is a probabilistic model that can predict what values of the parameters have the maximum likelihood to recreate the observed dataset. This is represented by the following formula:

For linear regression, our assumption is that the dependent variable has a linear relationship with the model. MLE assumes that the dependent variable values have a normal distribution. The idea is to predict the parameters for each observed value of X so that it models the value of y. We also estimate the error for each observed value that models how different the linear predicted value of y is from the actual value.