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Linear & Polynomial Regression

July 8, 2026 · Updated: July 8, 2026

This tool fits regression models to your data and provides detailed statistics including coefficient estimates, standard errors, p-values, R², ANOVA, and residual diagnostics. A scatter plot with the fitted curve is generated for visual inspection.

Linear & Polynomial Regression

How to Use

  1. Enter X and Y values in the text areas — comma, space, or newline separated. Both columns must have the same number of values (at least 3).
  2. Select a model from the dropdown.
  3. Click Calculate to generate the results and plot.
  4. Use the Predict box to estimate y for a new x value.

Models

Model Equation Use case
Linear y = a + bx Simple linear relationship
Quadratic y = a + bx + cx² Curvature with one bend (≥ 4 points)
Cubic y = a + bx + cx² + dx³ Two bends (≥ 5 points)
Exponential y = a·e^(bx) Growth/decay (y > 0)
Power y = a·x^b Allometric scaling (x > 0, y > 0)
Logarithmic y = a + b·ln(x) Saturating relationship (x > 0)

Output

  • Equation with fitted coefficients
  • Coefficient table with estimate, standard error, t-statistic, and p-value
  • Goodness of fit: R², adjusted R², F-statistic with p-value
  • ANOVA table: decomposition of variance into regression and residual components
  • Residuals table (collapsible) with fitted values and residuals; points with |standardized residual| > 2 are flagged
  • Scatter plot with fitted curve and R² annotation