The choice between linear and nonlinear regression is really a question about the shape of your data. Get it right and the fit is excellent; force a line onto a curve and even a powerful regression calculator will give you a poor model.
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What linear regression assumes
Linear regression fits y = A + Bx: a constant rate of change B. Every one-unit increase in x changes y by the same amount. That's perfect for relationships like cost = fixed + (rate × quantity).
Data (1,3), (2,5), (3,7) fits y = 2x + 1 with r = 1 — a flawless straight line.
When you need a curve
Many real relationships bend. The STAT mode offers several nonlinear shapes:
| Model | Behaviour | Typical data |
|---|---|---|
| Quadratic | Rises then falls (or vice versa) | Projectile height, optimisation |
| Logarithmic | Fast then flattening | Diminishing returns |
| Exponential | Constant percentage growth | Populations, compound interest |
| Power | Scaling law | Area vs length, physics laws |
| Inverse | Decays toward an asymptote | Speed vs time for fixed distance |
How to tell the difference
- Plot first. If the cloud of points curves, a line won't do.
- Check r. A low correlation on a linear fit, despite an obvious pattern, signals nonlinearity.
- Look at residuals. A good linear fit scatters residuals randomly; a U-shaped residual pattern means you've linearised a curve.
How a calculator fits curves
Exponential, power and logarithmic models are linearizable — taking logs turns them into straight lines — so the calculator fits them with the same least-squares machinery and reports A, B and r. Switch to STAT mode, choose the model, and enter your paired data. Comparing fits is covered in choosing the right regression model, and the full STAT workflow is in the statistics calculator pillar guide.
Frequently asked questions
Linear vs nonlinear — what's the difference?
Linear fits a straight line with constant slope; nonlinear fits a curve whose rate of change varies.
How do I know my data is nonlinear?
Plot it; a bend, low linear r, or a patterned residual plot all point to a curve.
Can a calculator fit nonlinear models?
Yes — exponential, power and log models are linearizable and fit directly in STAT mode.
Fit your data both ways
Try a linear and a nonlinear model in STAT mode and compare the r values.
Open the regression calculator →