Data Input
Sample Data
x, y (one point per line, comma or tab separated, max 50 points)
Regression Type
Prediction
Predicted Y = —
—
R² Coefficient
—
RMSE
—
Data Points
—
Predicted Y
Regression Equation
—
Scatter Plot + Regression Curve + Residuals
Theory
Linear regression $y = ax + b$:
$$a=\frac{n\sum x_i y_i-\sum x_i\sum y_i}{n\sum x_i^2-\left(\sum x_i\right)^2}$$Coefficient of determination: $R^2 = 1 - \dfrac{SS_{res}}{SS_{tot}} = 1 - \dfrac{\sum(y_i-\hat{y}_i)^2}{\sum(y_i-\bar{y})^2}$
RMSE: $\sqrt{\dfrac{1}{n}\sum(y_i-\hat{y}_i)^2}$
Polynomial: solved via normal equations (Vandermonde matrix).
Exponential: linearize via $\ln y = \ln a + bx$, then apply linear regression.
Applications: S-N fatigue curve fitting (power law) / Stress-strain curve approximation / FEM response surface method / Nusselt-Reynolds correlation / Material constant identification from test data.