Exponential Regression Calculator

What Is Exponential Regression?

Exponential regression finds the curve $y = ab^x$ that best fits a set of data points. It is useful when values grow or decay by a constant factor per unit increase in $x$, such as investment growth, cooling temperatures, or radioactive decay. Compare with Linear Regression Calculator or Cubic Regression Calculator.

How It Works

Take the natural log of both sides: $\ln(y) = \ln(a) + x\ln(b)$. Fit a straight line to $(x, \ln(y))$ using least squares, then recover $a = e^c$ and $b = e^m$.

Example

Points $(1,2), (2,5), (3,12), (4,25), (5,50)$ follow roughly $y \approx 1.2 \times 2.3^x$. The $R^2$ value shows how well the curve fits the data.

Frequently Asked Questions

Why must y values be positive?

The natural logarithm is only defined for positive numbers. Zero or negative y values cannot be used in exponential regression.

What does R-squared mean?

$R^2$ measures fit quality from 0 to 1. Values closer to 1 mean the exponential model explains more of the variation in the data.

What is the difference between growth and decay?

When $b > 1$ the model describes exponential growth. When $0 < b < 1$ it describes exponential decay.

How many points do I need?

At least three $(x, y)$ pairs. More points generally produce a more reliable fit.

Can I use this for prediction?

Yes. Plug any $x$ into $y = ab^x$ to estimate the corresponding value, but be cautious extrapolating far beyond your data range.

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