Polynomial Regression Calculator
Enter Data Points: Provide dataset as pairs of x and y values in the format: x1,y1;x2,y2;.... example: 1,2;2,4;3,9.
Enter Polynomial Degree: Specify degree of polynomial (e.g., 2 for quadratic or 3 for cubic).
The calculator will compute and display polynomial equation and coefficients.
Polynomial Regression Formula
The form of the polynomial regression equation is:
y = β₀ + β₁x + β₂x² + β₃x³ + ... + βₙxⁿWhere:
- y is the dependent variable
- x is the independent variable
- β₀ is the y-intercept
- β₁, β₂, β₃, βₙ are coefficients
- n is the polynomial degree
Different Polynomial Degrees:
- Linear (n=1): y = β₀ + β₁x
- Quadratic (n=2): y = β₀ + β₁x + β₂x²
- Cubic (n=3): y = β₀ + β₁x + β₂x² + β₃x³
- Quartic (n=4): y = β₀ + β₁x + β₂x² + β₃x³ + β₄x⁴
Matrix Formulas
To compute the coefficients a₀, a₁, …, aₙ, we use:
a = (X^T X)⁻¹ X^T * YWhere:
- X is the design matrix, where each row corresponds to the powers of x for a given data point.
- Y is the column matrix of y values.
- X^T is the transpose of X.
- (X^T * X)⁻¹ is the inverse of the product of X^T and X.
What is Polynomial Regression?
Polynomial regression is a form of regression analysis where the relationship between the independent variable x and the dependent variable y is modeled as an nth-degree polynomial. It’s used when data points show a curvilinear relationship, making it more suitable than simple linear regression for many real-world applications.