Exponential Regression Calculator

Find the exponential curve of best fit for your data points using the form y = a × b^x

Data Points Input

⚠️ Enter at least 3 valid data points (y values must be positive) to calculate regression.

Valid data points: 0 of 5

Example: Population Growth

Sample Data

Years (x):

0, 1, 2, 3, 4, 5

Population (y):

100, 150, 225, 338, 506, 759

Expected Result

Equation: y = 100.0 × 1.500^x

R²: ≈ 1.000 (perfect exponential fit)

Interpretation: Population grows by 50% each year

How to Use

1

Enter Data

Input at least 3 data points (y values must be positive)

2

Set Precision

Choose number of significant figures for coefficients

3

View Results

Get exponential equation and fit statistics

Features

Supports up to 30 data points

Automatic R-squared calculation

Adjustable precision (2-6 sig figs)

Growth/decay interpretation

Model quality assessment

Understanding Exponential Regression

What is Exponential Regression?

Exponential regression finds the exponential curve that best fits a set of data points. The exponential model follows the form y = a × b^x, where data grows or decays at a rate proportional to its current value.

When to Use

  • Population growth or decline
  • Radioactive decay
  • Compound interest calculations
  • Temperature cooling/heating
  • Viral spread modeling

Mathematical Method

1. Transform data: Convert (x, y) to (x, ln(y))

2. Linear regression: Find ln(y) = c + mx

3. Convert back: a = e^c, b = e^m

4. Final equation: y = a × b^x

Note: All y-values must be positive for logarithmic transformation

Interpreting Results

Coefficient 'a'

The y-intercept when x = 0. Represents the initial value or starting point of the exponential process.

Base 'b'

Growth/decay factor. If b > 1: exponential growth. If 0 < b < 1: exponential decay.

R-squared

Goodness of fit. Values closer to 1 indicate better exponential model fit to the data.