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DATA POINTS — all y values must be positive
X Value
Y Value
REGRESSION EQUATION
a (coefficient)
b (growth base)
Prediction
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How Exponential Regression Works

Exponential regression finds the best-fit curve of the form y = ab^x for your data. It is used to model exponential growth (population, investments, viral spread) or decay (radioactive material, depreciation).

Linearize: ln(y) = ln(a) + x·ln(b) → apply OLS → convert back
By taking ln(y), the equation becomes linear. Ordinary Least Squares regression finds the optimal slope (ln b) and intercept (ln a), then a = e^intercept and b = e^slope.
R² ValueFit QualityInterpretation
0.95 – 1.00ExcellentStrong exponential relationship
0.80 – 0.94GoodReasonably well-fitted curve
0.60 – 0.79ModerateSome exponential trend present
Below 0.60WeakTry linear or power regression

Frequently Asked Questions

Use it when your data increases or decreases at a proportional rate per unit. Real-world examples: bacterial colony growth, compound interest portfolios, radioactive decay, viral social media posts, technology adoption curves, and COVID-19 case counts early in an outbreak.

Exponential regression requires all y values to be strictly positive because we take ln(y). If your data includes zeros or negatives, you cannot use exponential regression directly. Consider shifting data upward or using a different model.

The base b is the multiplicative growth or decay factor per unit increase in x. If b > 1, y grows exponentially. If 0 < b < 1, y decays. For example, b = 2.718 means y approximately triples per unit x.

Linear regression fits y = mx + b (additive change — constant increase per unit x). Exponential regression fits y = ab^x (multiplicative change — proportional increase per unit x). Exponential models apply when percent change is constant.

R² above 0.95 is excellent. Above 0.80 is good. Below 0.60 suggests the data does not follow an exponential pattern well — try comparing with linear or power regression.

Yes, but with caution. Exponential regression is useful for short-term forecasting of exponentially-trending data. However, true exponential growth cannot continue indefinitely — long-range forecasts should be treated as upper bounds.

Sources & Methodology
Uses ordinary least squares regression on log-transformed y values to compute optimal parameters a and b for y = ab^x.
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OLS Regression via Log Linearization
Standard method: take ln(y), apply linear regression, convert back via exp(). Requires all y > 0.
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Devore & Berk — Modern Mathematical Statistics
Reference for non-linear regression via linearization and R-squared calculation on transformed data
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Khan Academy — Exponential Regression
Educational reference for exponential curve fitting methodology and interpretation
Last updated: March 2026
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