What Is Linear Regression? Explanation with Examples

One of the most basic methods in machine learning and statistics is linear regression, which is used to predict the connection between one or more independent variables and a dependent variable. It is extensively used in many different industries for data analysis, decision-making, and predictive modelling.

Understanding Linear Regression

A statistical technique called linear regression is used to determine a link between one or more independent variables, often referred to as features or predictors, and a dependent variable, also known as the target variable. It is simpler to forecast the value of the dependent variable based on the input values as the relationship is represented by a linear equation.

To put it simply, linear regression looks for a straight line on a scatter plot that best fits the data points. By reducing the discrepancy between the actual and anticipated values, this line—also referred to as the regression line—is found.

The Equation of Linear Regression

The equation for simple linear regression (when there is only one independent variable) is:

Where:

• Y is the dependent variable (target variable).

• X is the independent variable (predictor).

• ​ is the intercept (value of Y when X = 0).

• ​ is the slope (rate of change of Y with respect to X).

• ϵ is the error term (difference between actual and predicted values).

For multiple linear regression (when there are multiple independent variables), the equation is:

Types of Linear Regression

1. Basic Linear Regression

One independent variable and one dependent variable are involved in simple linear regression. It looks for a straight line that best depicts the relationship between the data points.

2. Regression with Multiple Linear

By adding two or more independent variables, multiple linear regression goes beyond ordinary linear regression. This makes it possible to model real-world data in a more sophisticated way, accounting for the effects of many factors on the dependent variable.

Assumptions of Linear Regression

For linear regression to be valid, the following assumptions should be met:

• Linearity: There should be a linear relationship between the independent and dependent variables.

• Independence: It is important for observations to stand alone from one another.

• Homoscedasticity: The residuals' (errors') variance should be constant throughout a range of independent variable values.

• Error Normality: The residuals ought to have a normal distribution.

• No Multicollinearity: Independent variables in multiple linear regression shouldn't have a strong correlation with one another.

Example of Linear Regression: Predicting House Prices

Let's say you wish to estimate a home's cost based on its dimensions. The house's size would be the independent variable (X) in a simple linear regression model, which would then apply a best-fit line to forecast the price (Y).

To increase the forecast accuracy of multiple linear regression, other variables such as the house's age, location, and number of bedrooms can be added.

Applications of Linear Regression

Linear regression is widely used in various fields, including:

• Finance: Forecasting sales income, interest rates, or stock values.

• Healthcare: Calculating how long a patient will take to recover depending on their age and therapy.

• Marketing: Examining how advertising expenditures affect sales income.

• Economics: Researching the connection between inflation and GDP growth.

Conclusion

One effective method for simulating and forecasting interactions between variables is linear regression. It is a crucial method in data science and machine learning because of its efficacy, interpretability, and simplicity.Do you want to become an expert in data science and predictive modelling? Enrol in our courses to get started on your educational path right now!