Linear Regression

Linear regression is a statistical analysis method for predicting the value of one variable (dependent) based on the value of another (independent). It is a fundamental type of predictive analysis, particularly used in machine learning and data modeling. The predicted line in linear regression is straight, signifying a linear association between variables.

How Linear Regression work

Linear regression works by fitting a "best-fit" line through the data points in a scatter plot. The line is established based on the relationship between the independent (predictor) and dependent (response) variables. The line equation is usually expressed as Y = a + bX, where 'Y' is the dependent variable, 'X' is the independent variable, 'b' is the slope (the rate of change), and 'a' is the y-intercept (the predicted value of Y when X=0).

The "best" line (i.e., minimizing the amount of error or the difference between the real data point and the point on the line) is determined using a method called "least squares". This method calculates the shortest distance between the actual data points and their corresponding points on the predictive line and iteratively adjusts the line's parameters (slope and intercept) to minimize that distance.

Linear regression makes assumptions about the data, such as independence of observations, homoscedasticity (equal variance of errors), and normality of errors. Checking for, and addressing violations of these assumptions, is an important part of applying linear regression in practice.

Linear regression can be simple (one independent variable) or multiple (more than one independent variable). It can be used for both binary classification and continuous predictions, making it versatile for a range of problems in data science, economics, social sciences, and beyond.