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
Enter Data
Input at least 3 data points (y values must be positive)
Set Precision
Choose number of significant figures for coefficients
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.