Example of Linear Regression in Real Life

You might have read lot of tutorials on Linear Regression and already have the assumption - Linear Regression is not easy to Understand. We will make Linear Regression very easy for you. Let's boil down each concept and learn with help of Examples. If you have no idea what Linear regression is, this tutorial will be help you understand the basics.

Linear regression might sound like a complex term, but it’s actually a very simple concept. Linear Regression is all about finding patterns in data. When two things are connected, (like - hours of study and test scores, OR temperature and ice cream sales) linear regression helps us understand and predict how one affects the other.

Basically, Linear Regression is asking if Thing-1 will change, how Thing-2 will respond? Answer of this question is often found by drawing a straight line through data points on a graph.

How Does Linear Regression Work?

Linear regression helps us answer questions about relationships in data. For example:

• Is there a consistent connection between the amount of time you spend studying and your test scores?
• Can we predict future trends based on past data?

This is done by identifying two types of variables:

• Independent Variable: The thing we control or know (e.g., hours studied).
• Dependent Variable: The thing we want to predict (e.g., test scores).

Linear regression tries to find the best-fit line through the data. This line is like a rule or formula that tells us:

When the independent variable (e.g., hours studied) increases, how much does the dependent variable (e.g., test scores) increase or decrease?
If we know the independent variable’s value, what’s the most likely value for the dependent variable?

What is Best Fit Line?

Among all possible lines you could draw through the data, linear regression finds the one that minimizes the errors (the gaps between the line and the points). This is called the line of best fit.

Understand Linear Regression with Help of Example

The more time you spend in studying, the better your test scores. Linear regression helps us find the relationship between these two things and use that relationship to make predictions.

Think of it like this:

• You collect some data: how many hours you studied and the scores you got on tests.
• You plot this data on a graph.
• Then, you draw a straight line through the points in such a way that it’s as close as possible to all the points. This line shows the trend.

Once you have this line, you can use it to make predictions. For example, if you studied 5 hours for a test, the line can help you estimate what score you’re likely to get.

Intuition Behind Linear Regression

Let’s say you’re tracking how much time you spend studying and the test scores you get. You gather the following data:

Hours of Study Test Score

2 50

4 70

6 90

If you plot this data on a graph:

• The x-axis represents the hours of study.
• The y-axis represents the test score.

You will see the points roughly form a straight-line pattern. Linear regression helps us draw the best possible straight line through these points. Once we have the line, we can use it to predict scores for other study hours, like 3, 5, or even 8 hours.

Math Behind Linear Regression

The equation of a straight line is:

y = mx + c

where,

y: The value we want to predict (your test score).
x: The value we know (hours of study).
m: The slope of the line (how much yy changes when xx changes by 1 unit).
c: The y-intercept (the value of yy when x=0x=0).