Definition and application of OLS regression

Ordinary Least Squares (OLS) regression is an optimization strategy designed to find the closest straight line to the data points in a linear regression model. OLS is widely regarded as the most effective optimization method in linear regression models because of its ability to provide unbiased estimates of alpha and beta. By minimizing the sum of squares of the residuals, OLS can find the optimal parameter values ​​so that the regression line has the highest fitting degree to the data points. This method not only helps us understand the relationship between independent variables and dependent variables, but also allows for predictive and inferential analysis. Overall, OLS regression is a simple yet powerful tool that can help us explain and predict

How OLS is applied to linear regression

Linear regression is a method used in supervised machine learning Algorithm for the task. It is mainly applied to regression problems, not classification problems. Regression problems involve predicting continuous values, while classification problems predict categories. Therefore, the goal of the linear regression algorithm is to predict a continuous target variable by building a linear model. Unlike classification, the target variable is not a categorical value, but a numerical or continuous value. Through the linear regression algorithm, we can predict a continuous number based on the linear relationship of the input variables to model and predict the problem.

Regression tasks can be divided into two categories: one is a task that uses only one feature to predict the target, and the other is a task that uses multiple features to predict the target.

How to find OLS in a linear regression model

The goal of simple linear regression is to minimize the error term by adjusting the parameters. Specifically, the model adopts the minimization of the squared error as the optimization objective. We don't want positive and negative errors to cancel each other out, as they will both penalize our model. Therefore, this process is called ordinary least squares (OLS) error.

In summary, OLS is an optimization strategy used to fit straight lines of data points. Although OLS is not the only optimization strategy, it is one of the most popular because it provides unbiased estimators of the actual values ​​of alpha and beta.

According to the Gauss-Markov theorem and the assumptions of the linear regression model, the OLS estimator is based on the linearity of the parameters, random sampling of observations, zero conditional mean, no multicollinearity and error homoskedasticity. is considered to be the best unbiased linear estimator.

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