Little Bits of Artificial Intelligence

1. What is Linear Regression?

• A method to find the best-fitting straight line through a set of data points.
• Helps predict outcomes (like scores, prices, etc.) based on input variables.

Simple Linear Regression:

• Equation: y=mx+c
• Where:
• y = predicted value
• x = input feature
• m = slope
• c = intercept

2. Real-Life Applications

Example 1: House Price Prediction

• Predict price based on size in square feet.

Example 2: Salary Estimation

• Predict salary based on years of experience.

3. Manual Implementation (Without Libraries)

Simple Linear Regression (1 variable)

• First python program shown in step 2 section using
• sum(x), sum(y), sum(x*y), sum(x^2)

4. Required Mathematical Concepts

To understand Linear Regression deeply, we should know:

1. Arithmetic operations: +, –, ×, ÷
2. Averages: Mean
3. Squares and square roots: x^2, sqrt{x}
4. Basic Algebra: Variables and equations
5. Summation notation: ∑x,∑xy
6. Line concepts: Slope and intercept
7. Correlation: How variables move together

5. Mind Map: Math ➝ Linear Regression

Visual roadmap (described):

Arithmetic
   ↓
Averages & Squares
   ↓
Algebra & Summation
   ↓
Slope & Intercept
   ↓
Correlation (Optional)
   ↓
→ Linear Regression

6. Multivariate Linear Regression (2+ variables)

Concept:

• When we want to predict based on multiple inputs (e.g., size & bedrooms):y=m1x1+m2x2+⋯+mnxn+c

Example:

• Predict house price from:
• x₁: Size in sqft
• x₂: No. of bedrooms

Final Thought:

Linear regression is a gateway to machine learning, and understanding it through basic math and real-world logic builds a strong foundation for future models like polynomial regression, logistic regression, and beyond.