Quadratic Polynomial Regression Model Solved Example in Machine Learning
Regression modeling is a process of determining a relationship between one or more independent variables and one dependent or output variable.
Example:
1. Predicting the price of the car given the car model, year of manufacturing, mileage, engine capacity.
2. Predicting the height of a person given the age of the person.
Polynomial Regression
Let there be only one independent variable x and the relationship between x, and dependent variable y, be modeled as,
y=a0+a1*x+a2*x2 +………+ +an*xn
for some positive integer n >1, then we have a polynomial regression.
Problem Deninition:
Find a quadratic regression model for the following data:
| X | Y |
| 3 | 2.5 |
| 4 | 3.2 |
| 5 | 3.8 |
| 6 | 6.5 |
| 7 | 11.5 |
Solution:
Let the quadratic polynomial regression model be
y=a0+a1*x+a2*x2
The values of a0, a1, and a2 are calculated using the following system of equations:
First, we calculate the required variables and note them in the following table.
| x | y | x2 | x3 | x4 | y*x | y*x2 | |
| 3 | 2.5 | 9 | 27 | 81 | 7.5 | 22.5 | |
| 4 | 3.2 | 16 | 64 | 256 | 12.8 | 51.2 | |
| 5 | 3.8 | 25 | 125 | 625 | 19 | 95 | |
| 6 | 6.5 | 36 | 216 | 1296 | 39 | 234 | |
| 7 | 12 | 49 | 343 | 2401 | 80.5 | 563.5 | |
| Σ | 25 | 27.5 | 135 | 775 | 4659 | 158.8 | 966.2 |
Using the given data we,
Solving this system of equations we get
a0=12.4285714
a1=-5.5128571
a2=0.7642857
The required quadratic polynomial model is
y=12.4285714 -5.5128571 * x +0.7642857 * x2
Now, given the value of x (independent variable), we can calculate the value of y (dependent or output variable).
Video Tutorial of Quadratic Polynomial Regression Model
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