di Sergio Mauri
Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. It assumes a linear relationship between the variables, meaning that the relationship can be represented by a straight line.
In simple linear regression, there is only one independent variable used to predict the dependent variable. The relationship between the variables is represented by a straight line equation of the form:
y = mx + b
Where:
- y is the dependent variable (the variable to be predicted)
- x is the independent variable (the variable used for prediction)
- m is the slope of the line (represents the relationship between x and y)
- b is the y-intercept (the value of y when x is 0)
The goal of linear regression is to estimate the values of m and b that minimize the difference between the predicted values (represented by the line) and the actual values of the dependent variable. This is typically done using a method called least squares, which finds the line that minimizes the sum of the squared differences between the predicted and actual values.
Linear regression can also be extended to multiple independent variables, resulting in multiple linear regression. In this case, the relationship between the variables is represented by a hyperplane instead of a line. The equation becomes:
y = b0 + b1x1 + b2x2 + … + bnxn
Where:
- y is the dependent variable
- x1, x2, …, xn are the independent variables
- b0, b1, b2, …, bn are the coefficients that represent the relationship between each independent variable and the dependent variable.
Linear regression is widely used in various fields, such as economics, social sciences, finance, and machine learning, for tasks like predicting sales, analyzing trends, and making forecasts.
