Least squares regression is a popular approach used in machine learning for fitting a linear model to a given dataset. It is a powerful statistical technique that involves finding the line of best fit to explain the relationship between two variables.

In simpler terms, linear regression is a methodology that establishes a relationship between a dependent variable and one or more independent variables. The objective of this technique is to find the line that best summarizes this relationship.

Least squares regression works by minimizing the sum of the squared distances between the observed and predicted values of the dependent variable. The equations used in linear regression are derived from the principle of least squares, which states that the best-fitting line should minimize the sum of the squared differences between the predicted and actual values.

The procedure for performing least squares regression involves obtaining the values of the independent variable and the dependent variable. The independent variable is the input, which is used to predict the value of the dependent variable or the output. The line of best fit is then calculated using the least squares method. This line can be used to make predictions about the dependent variable’s value based on the given independent variable values.

One key advantage of least squares regression is that it allows for predicting values for a dependent variable based on new independent variable values. This means that once we learn the relationship between the inputs and outputs, we can use it to make predictions for new data points, making it a valuable tool for making predictions in various fields such as finance, economics, and science.

Another significant use of least squares regression is in machine learning problems where there are multiple input variables. Multiple regression analysis involves estimating the relationship between the independent variables and the dependent variable, leading to a multidimensional line of best fit or hyperplane.

In conclusion, least squares regression is a powerful machine learning methodology used to establish a relationship between the dependent variable and one or more independent variables. This technique is widely used in various fields as it enables predictions for new data points, making it an essential tool for making predictions in different areas, including finance, economics, and science.