Which method is used to find the best fit line for linear regression?Maximum likelihoodLeast square errorMean square errorEither of A and B

Break Down the Problem

1. Identify the methods listed in the question.
2. Understand what each method implies in the context of linear regression.

Relevant Concepts

1. Maximum Likelihood: An estimation method that finds parameters of a statistical model that maximize the likelihood function, given the data.
2. Least Square Error: A method that minimizes the sum of the squares of the differences between observed and predicted values.
3. Mean Square Error: Similar to least squares, it calculates the average of the squares of errors—that is, the average squared difference between estimated and actual values.

Analysis and Detail

1. In linear regression, the primary goal is to find the best-fitting line through a set of data points.
2. The Least Squares method is widely used because it specifically minimizes the residuals' squared differences, providing the best linear unbiased estimator under certain conditions (Gauss-Markov theorem).
3. Maximum likelihood can also be applied depending on the distributional assumptions, but it is not the primary method traditionally used for simple linear regression.
4. Mean Square Error is a derived concept that evaluates the accuracy of an estimator, and although it shows how a model performs, it is not a method for fitting the line.

Verify and Summarize

The Least Square Error method is the primary technique used for finding the best fit in linear regression. While Maximum Likelihood can be applied under certain conditions, Least Squares is the standard method.

Final Answer

Least square error is the most commonly used method to find the best fit line for linear regression. Therefore, the correct option is Least square error.