What is exponential regression?
Exponential regression fits a curve of the form y = A· e^{Bx} to a set of paired data points. It is the standard tool for modeling quantities that grow or decay at a rate proportional to their current size, such as population growth, radioactive decay, compound interest, or bacterial cultures. This calculator is a pure mathematical and statistical tool, so it applies identically everywhere with no country-specific assumptions.
How to use it
Enter your independent values in the X values box and your dependent values in the Y values box, both as comma-separated numbers. The two lists must have the same number of entries, you need at least two points, and every Y value must be strictly positive (the method requires the natural logarithm of y). Choose the display precision, then read off the fitted coefficients A and B, the correlation coefficient r, and the assembled equation.
The formula explained
Because y = A· e^{Bx} is non-linear, we linearize it by taking natural logarithms: \ln y = \ln A + B· x. This is an ordinary linear regression of \ln(y) against x. Using the centered sums S_{xx} = \sum (x - \bar{x})^2, S_{yy} = \sum (\ln y - \overline{\ln y})^2, and S_{xy} = \sum (x - \bar{x})(\ln y - \overline{\ln y}), the slope is
Worked example
For x = [1, 2, 3, 4, 5] and y = [2.7, 7.4, 20.1, 54.6, 148.4] (roughly e^{x}), we get S_{xx} = 10, S_{xy} ≈ 10.0115, S_{yy} ≈ 10.0231. Then B ≈ 1.0012, A ≈ 0.9956, and r ≈ 1.0000. The fitted curve
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