Regression_basics_typesofregression.pptx

basic concepts of regression

1. Introduction to Regression • Regression is used to predict the value of one variable based on another. • It establishes a functional relationship between dependent (Y) and independent (X) variables.

2. Types of Regression • Simple Linear Regression: One independent variable. • Multiple Regression: Two or more independent variables.

3. Regression Line • The best-fit line representing the relationship between X and Y. Equation: Ŷ = a + bX where b = slope, a = intercept.

4. Least Squares Method • Minimizes the sum of squared residuals between observed and predicted Y values. • Ensures best possible line fit.

5. Formulas Slope (b) = Σ[(X - X̄)(Y - Ȳ)] / Σ(X - X̄)² Intercept (a) = Ȳ - bX̄

6. Example Problem Given data: X = [1,2,3,4,5], Y = [2,3,5,4,6] Step 1: Compute X̄ and Ȳ. Step 2: Find b = 0.8, a = 1.6 Equation: Ŷ = 1.6 + 0.8X

7. Interpretation of r² • r² = Coefficient of determination. • Explains proportion of variance in Y predicted from X. • Example: r² = 0.81 → 81% variation in Y explained by X.

8. Multiple Regression • Ŷ = a + b₁X₁ + b₂X₂ + ... + bₙXₙ • Useful when outcome depends on several factors.

9. Regression Toward the Mean • Extreme observations tend to move closer to the mean in subsequent measurements.

10. Applications of Regression • Forecasting sales, demand, prices. • Predicting academic performance. • Medical research and diagnostics.

11. Summary • Regression predicts dependent variable values. • Uses least squares method for best fit. • r² measures model accuracy.