What is Linear Regression? Towards Deep Learnings

3 min readJan 5, 2025

What is Linear Regression?

Linear Regression is like finding a straight-line rule to connect two things (variables) so you can predict one based on the other.

Real-Life Analogy: Pocket Money and Grades

Imagine this: You notice that the more pocket money your parents give you, the better your grades are because you can afford better study materials.

For example:

₹100 = 60% marks
₹200 = 70% marks
₹300 = 80% marks

Here’s the pattern: Marks = 50 + (0.1 × Pocket Money)

If you get ₹400, you can predict your marks: Marks = 50 + (0.1 × 400) = 90%.

This straight-line rule is Linear Regression!

How Does It Work?

Data Points: These are the values you know (e.g., pocket money vs. grades).
Straight Line: Linear Regression tries to draw a straight line through the data points.
Prediction: Once you have the line (or equation), you can predict new values.

In math, the straight line is written as: y = mx + c where:

y is what you predict (grades).
x is what you already know (pocket money).
m is the slope (how much grades change with money).
c is the intercept (marks even with no pocket money).

Real-Life Example: Selling Lemonade

Imagine you’re selling lemonade.

If you sell 1 glass, you earn ₹10.
If you sell 2 glasses, you earn ₹20.
If you sell 3 glasses, you earn ₹30.

The pattern here is: Earnings = ₹10 × Number of glasses sold.

This is Linear Regression because:

Earnings (y) depend on the Number of glasses (x).
It’s a straight-line relationship.

How Linear Regression Looks on a Graph

If you plot the lemonade example:

The x-axis is the number of glasses sold.
The y-axis is the earnings.
The points will form a straight line (e.g., 1 glass = ₹10, 2 glasses = ₹20).

Linear Regression finds that line and gives you the formula: Earnings = ₹10 × Glasses Sold.

Why Linear Regression is Important?

It helps you:

Predict future outcomes. (How much will you earn if you sell 10 glasses?)
Understand Relationships between variables. (How does pocket money affect grades?)

Practical Example with Python

Let’s predict the marks of a student based on study hours.

# Step 1: Import libraries
from sklearn.linear_model import LinearRegression
import numpy as np
# Step 2: Input data
study_hours = np.array([1, 2, 3, 4, 5]).reshape(-1, 1)  # Hours studied
marks = np.array([50, 60, 70, 80, 90])  # Marks scored
# Step 3: Train the Linear Regression model
model = LinearRegression()
model.fit(study_hours, marks)
# Step 4: Predict marks for a new value
new_study_hours = np.array([[6]])  # Predict marks for 6 hours of study
predicted_marks = model.predict(new_study_hours)
# Step 5: Print the result
print(f"If you study for 6 hours, your predicted marks are {predicted_marks[0]:.2f}.")

Output:

If you study for 6 hours, your predicted marks are 100.00.

How is Linear Regression Related to Deep Learning?

Linear Regression is the foundation of many machine learning and deep learning techniques. Neural networks often use linear equations in layers to model complex relationships. It’s like building a house where Linear Regression is the first brick.

Summary

Linear Regression is a simple way to connect two things (variables) with a straight-line relationship. It’s used to predict future values and understand patterns. Whether it’s predicting grades, earnings, or sales, Linear Regression is a powerful yet easy tool to get started with! 🚀