Exponential Regression Calculator
Fit y = a * e^(bx) to your data by linearizing with ln(y).
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Enter X values and Y values separated by commas or spaces. All Y values must be positive (required for the natural log transformation). The calculator linearizes the model by taking ln(y), fits a line to (x, ln(y)), then converts back to get the exponential coefficients.
The result is an equation of the form y = a * e^(bx), where a is the initial value and b is the growth (or decay) rate.
About Exponential Regression
Exponential regression fits a curve of the form y = ae^(bx) to data that shows exponential growth or decay. It works by transforming the equation to ln(y) = ln(a) + bx, which is linear. The method then applies ordinary least squares to the transformed data. Common applications include population growth, radioactive decay, and compound interest modeling.
Frequently Asked Questions
Why must all Y values be positive?
The method requires taking the natural logarithm of Y values. Since ln(y) is undefined for y <= 0, all Y values must be strictly positive for exponential regression.
How do I know if exponential regression is appropriate?
Plot ln(y) against x. If the points form a roughly straight line, exponential regression is a good fit. Also compare R-squared values with linear or polynomial fits to see which model explains more variance.
What does a negative b value mean?
A negative b indicates exponential decay. The function decreases as x increases. A positive b indicates exponential growth.