📈 Exponential Regression Calculator
Fit a best-fit exponential curve (y = ae^bx) to your data. Enter five x,y data points (with positive y values) to get the coefficients a and b.
What This Calculator Does
Exponential regression fits a curve of the form y = a·e^(bx) to a set of data points, which is the standard shape for modeling growth or decay processes like population growth, compound interest, or radioactive decay.
How the Math Works
Fitting an exponential directly is difficult, so this calculator linearizes the problem by taking the natural log of both sides: ln(y) = ln(a) + bx. This turns it into an ordinary linear regression between x and ln(y), solved with the standard least-squares slope and intercept formulas, then converted back with a = e^(intercept).
- b (the slope of the linearized fit) = [n·Σ(x·ln y) − Σx·Σ(ln y)] / [n·Σx² − (Σx)²]
- a = e^(the linearized intercept)
- R² shows how well the exponential curve explains the variation in the logged data (closer to 1 is a better fit)
This method requires all y values to be positive, since the natural log of zero or a negative number is undefined. For general educational and analytical use.