# Linear Regression

## Definition of Linear Regression

Linear Regression: Linear Regression is a statistical technique that helps us understand how one variable (the dependent variable) changes when other variables (the independent variables) change. It does this by fitting a line through a set of data points, and then using the line to predict the value of the dependent variable for new data points.

## How is Linear Regression used?

Linear Regression is a powerful statistical technique used to identify the linear relationship between a dependent variable and one or more independent variables. It is used to predict the value of a continuous dependent variable based on values of independent variables. For example, in marketing a business may use linear regression to predict future sales based on factors like customer demographics, pricing, seasonality, and advertising spend.

Linear regression uses an equation with its coefficients as parameters that best fit the data. The equation estimates the relationship between two or more variables as a straight line. It is expressed as y = mx + b, where y represents the dependent variable (the one being estimated), m represents the slope of the line and b represents the intercept (where it crosses the y-axis).

The goal of linear regression is to determine values for m and b such that when all independent variables are plugged into the equation, they provide an estimate of the dependent variable which closely matches observed data points. This parameter estimation process requires optimization algorithms like gradient descent to find optimal values for both m and b.

Once these parameters have been determined, linear regression can be used for predictive purposes by plugging in new values for each independent variable and solving for y. Multiple linear regression allows multiple independent variables, but because this can result in overfitting models it’s important to consider other modeling techniques such as logistic regression or polynomial regression when dealing with large datasets.