Least Squares Regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. It helps to find the line of best fit that minimizes the sum of the squared residuals (the difference between the observed and predicted values).
Least Squares Regression is used when there is a need to understand the relationship between a continuous dependent variable and one or more independent variables. It can be used for prediction, forecasting, and determining the strength of the relationship between variables.
Simple Linear Regression is a special case of Least Squares Regression where there is only one independent variable. In Simple Linear Regression, the relationship between the dependent and independent variables is modeled using a straight line. On the other hand, Least Squares Regression can accommodate multiple independent variables and can model more complex relationships.
The main assumptions of Least Squares Regression are that the relationship between the dependent and independent variables is linear, the errors are normally distributed, and the errors have a constant variance. Additionally, the independent variables should be independent of each other, and there should be no multicollinearity (high correlation) between them.
The quality of the Least Squares Regression model is evaluated using various metrics such as the coefficient of determination (R-squared), root mean squared error (RMSE), and mean absolute error (MAE). These metrics help to assess how well the model fits the data and how accurately it predicts the values of the dependent variable.