Linear Regression Lecture Notes

Introduction

• Today's Topic: Linear Regression
• Video Introduction: A simple question - Do you know about Linear Regression?
• Reference to Previous Video: An older video on Linear Regression is available in the description.

What is Linear Regression?

• It is a statistical method used to understand relationships between data.
• Main Formula: y = bx + a
  • Where,
    • b: Slope
    • a: Intercept

Format of the Question

• You will be given a dataset.
• The dataset will include two attributes/columns.

Solution Process

1. Identify Unknowns:
   • We need to find the values of b and a.
2. List of Necessary Information in Brief:
   • Summation of x
   • Summation of y
   • Summation of xy
   • Summation of x²
3. Expand the Table:
   • Add columns of x² and xy along with x and y.
4. Calculate Summations:
   • For example:
     • Summation of x = 10
     • Summation of y = 19
     • Summation of xy = 54
     • Summation of x² = 30
5. Calculate a and b:
   • Formula for a:
     [ a = \frac{(Σy * Σx² - Σx * Σxy)}{n * Σx² - (Σx)²} ]
   • Formula for b:
     [ b = \frac{(n * Σxy - Σx * Σy)}{(n * Σx² - (Σx)²)} ]

Example Calculation

• How to calculate a and b from the given data:
  1. Calculate b:
     • n = 4
     • Σxy = 54
     • Σx = 10
     • Σy = 19
     • Σx² = 30
     • Result: b = 1.3
  2. Calculate a:
     • Σy = 19
     • b = 1.3
     • Σx = 10
     • Result: a = 1.5

Conclusion

• Final Equation: y = 1.3x + 1.5
• Alternative Formula:
  • If the basic equation seems complex: [ a = Σy - b * Σx / n ]
  • Calculate b first and then a.*

Summary

• Linear Regression shows the relationship between a dataset.
• Perform calculations and use equations for accurate results.
• It is important to use both equations correctly.