What is Regression Calculator?

Regression Calculator fits linear, quadratic, and polynomial curves to your data points. It computes coefficients, R² values, and standard errors, then plots the fitted curve alongside your data for visual analysis.

Six model types are available: linear, quadratic, polynomial (degree 3-10), exponential, logarithmic, and power. Paste rows from a spreadsheet directly, the parser accepts commas, tabs, or whitespace as separators. The chart overlays the fitted curve on the scatter, and the equation appears below in the form you'd cite in a paper.

How to use

1. Enter data points as X,Y pairs or paste from a spreadsheet.
2. Select the regression type (linear, quadratic, polynomial) and degree.
3. View the equation, R² statistic, residual plot, and download results.

When to use

• Checking whether a science fair dataset is a better fit for linear or quadratic.
• Estimating the exponent in a power-law relationship from physics lab measurements.
• Sanity-checking a trend line before pasting numbers into a business report.

Result

A researcher enters 20 temperature-vs-yield data points, selects quadratic regression, and gets y = -0.03x² + 4.2x - 12.5 with R² = 0.94, confirming a non-linear relationship.

FAQ

What does the R² value actually mean?

R² is the share of the variation in your Y values that the model explains. R² = 0.94 means 94% of the up-and-down in Y is accounted for by X; the other 6% is noise or other factors. R² near 1 looks great, but a high R² on a polynomial can also signal overfitting.

When should I use polynomial regression instead of linear?

Use polynomial only when the scatter plot has a clear curve and you have a physical reason for it. Adding higher-degree terms will always raise R² mechanically, but the curve starts wiggling between data points in ways that don't generalize. Start with degree 2; rarely go above 4.

What's the difference between exponential and power regression?

Exponential is y = a·e^(bx), so Y grows at a percentage rate as X increases (bacteria, compound interest). Power is y = a·x^b, so Y grows proportional to X raised to a constant exponent (planet orbital periods, allometric scaling). They look similar on linear axes but very different on log scales.

Can I do logarithmic regression with zero or negative X values?

No. Log regression fits y = a + b·ln(x), and ln(x) is undefined at x = 0 and negative x. Shift your data so all X values are positive, or pick linear/quadratic instead. The calculator will return an error if you try.

How many data points do I need for a reliable fit?

Two points fit a line perfectly but tell you nothing about scatter. Aim for at least 8-10 points for linear, more for higher-degree models. Rule of thumb is at least 10 points per coefficient you're estimating. With fewer, the R² overstates how good the model really is.

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