Practice Linear regression

Lessons, exercises, and projects about linear regression

To better understand what a **linear regression** is, imagine you have a group of points on a graph. These points represent some relationship between two things. For example, they could be the hours you study and the grades you get on an exam. Linear regression tries to find a straight line that passes as close as possible to all those points. This line is called the "regression line." ## Why represent regression as a line? We use a line because it is the simplest way to show a relationship between two things. If study hours and grades are related, a line can give us a general idea of how one thing changes when the other changes. ## Basic components of linear regression 1. **Variables**: - **Independent variable (X)**: This is what you control. In our example, it would be the hours of study. - **Dependent variable (Y)**: This is what you want to predict or explain. In our example, it would be the exam grade. 2. **Line of best fit**: This line is drawn in such a way that the sum of the vertical distances from all the points to the line is as small as possible. ## Simple example Suppose you have this data: - 1 hour of study -> 60 points on the exam - 2 hours of study -> 70 points on the exam - 3 hours of study -> 80 points on the exam - 4 hours of study -> 90 points on the exam If you plot these on a graph, the points would be almost in a straight line. Linear regression would find that line that passes through these points. ## The formula of the line The regression line can be described with a simple mathematical formula: \[ Y = a + bX \] Where: - **Y** is the grade we want to predict. - **a** is the point where the line crosses the Y-axis (when X is 0). - **b** is the slope of the line, which tells us how much Y changes when X changes. ## What is it for? Linear regression is used to predict values. For example, if you want to know what grade you might get if you study for 5 hours, you can use the formula of the line. It is also used to understand the relationship between two variables.