1. Polynomial Regression

2. Prototype
Consider steel hardness as a function of the amount of copper included in the alloy.

3. Linear Regression

4. Linear Regression

5. Polynomial
Clearly, copper content does impact steel hardness but it does not appear linear. Consider a quadratic fit.

6. Polynomial Regression

7. Residuals Must be Done Manually

8. Summary SLR R2 = 0.023 F= 0.187 Quadratic R2 = 0.545 F=4.199
Let’s try a polynomial of size n

9. Polynomial of Size n SLR R2 = 0.023 F= 0.187
Quadratic R2 = F=4.199
Let’s try a polynomial of size n

10. 5th order Polynomial

11. 5th order Polynomial