Use this calculation to reproduce a defined quantitative method when the observations, units, sampling process, and assumptions match the method shown here.

X values

Required list. Independent variable values.

Y values

Required list. Dependent variable values aligned with x.

Degree

Optional integer. Polynomial degree between 1 and 6.

The cited overview of Regression analysis supplies background for the terminology and domain context used by this tool.^[1]

Least-squares polynomial regression (degree 1 to 6) solved exactly through the normal equations with partial pivoting; reports ascending-power coefficients and R². Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

Coefficients

Returned list. Fitted coefficients in ascending powers c0..cd.

R squared

Returned number. Coefficient of determination R² (defined as 1 for constant y).

• A numerical result does not by itself establish data quality, causation, representativeness, independence, distributional fit, or practical significance.
• Degree must be at least 1.
• Degree must be no greater than 6.
• Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.

Inspect the underlying data, visualize its distribution, report uncertainty and sample size, and compare the result with a robust or domain-specific method where appropriate.

• Linear Regression Calculator

  Fit an ordinary least-squares line to paired samples and report slope, intercept, and R squared.

• Ridge Regression Demonstrator

  Fit a one-feature ridge regression with an unpenalized intercept.

• Pearson Correlation Calculator

  Calculate Pearson's linear correlation coefficient for two paired numeric series.