Exponential Regression Calculator
Calculate exponential regression using your data.
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What this tool does
Calculate exponential regression using your data. Log-linear least squares. Constant percentage growth is assumed; the log-scale fit weights relative errors, so it differs from a direct nonlinear least-squares fit.
How to use the Exponential Regression Calculator
- Enter or select x values (comma or whitespace separated).
- Enter or select y values (positive, same order as x).
- Enter or select predict y at x =.
- Read the calculated result; change any measurement to compare alternatives.
Formula
fit ln(y) = ln(a) + b·x by least squares, so y = a·e^(b·x); R² is reported on the log scale
- x
- X values (comma or whitespace separated)
- y
- Y values (positive, same order as X)
- x0
- Predict Y at X =
Log-linear least squares. Constant percentage growth is assumed; the log-scale fit weights relative errors, so it differs from a direct nonlinear least-squares fit.
Worked example
For exponential regression calculator, the following measurements illustrate the exact method: X values (comma or whitespace separated): 0,1,2,3,4; Y values (positive, same order as X): 3,5,8,13,21; Predict Y at X =: 5.
Inputs
- X values (comma or whitespace separated)0,1,2,3,4
- Y values (positive, same order as X)3,5,8,13,21
- Predict Y at X =5
Result
- Coefficient a3.03
- Growth rate b (per unit X)0.48
- Implied growth per unit X (%)62.37
- R² (log scale)1
- Predicted Y at the entered X34.25
Results explained
- Coefficient a
- Coefficient a from the formula above. Log-linear least squares. Constant percentage growth is assumed; the log-scale fit weights relative errors, so it differs from a direct nonlinear least-squares fit.
- Growth rate b (per unit X)
- Growth rate b (per unit X) from the formula above. Log-linear least squares. Constant percentage growth is assumed; the log-scale fit weights relative errors, so it differs from a direct nonlinear least-squares fit.
- Implied growth per unit X (%)
- Implied growth per unit X (%) from the formula above. Log-linear least squares. Constant percentage growth is assumed; the log-scale fit weights relative errors, so it differs from a direct nonlinear least-squares fit.
- R² (log scale)
- R² (log scale) from the formula above. Log-linear least squares. Constant percentage growth is assumed; the log-scale fit weights relative errors, so it differs from a direct nonlinear least-squares fit.
- Predicted Y at the entered X
- Predicted Y at the entered X from the formula above. Log-linear least squares. Constant percentage growth is assumed; the log-scale fit weights relative errors, so it differs from a direct nonlinear least-squares fit.
Frequently asked questions
fit ln(y) = ln(a) + b·x by least squares, so y = a·e^(b·x); R² is reported on the log scale
Log-linear least squares. Constant percentage growth is assumed; the log-scale fit weights relative errors, so it differs from a direct nonlinear least-squares fit.
Enter numbers only, in the units and format each label describes. Remove missing values rather than substituting zero, unless zero is a real observation.
No. Results describe the numbers you entered. Statistical inference also depends on sampling design, independence, model fit and interpretation; a p-value is not the probability that a hypothesis is true.
No. Every calculation, including the distribution algorithms, runs entirely in your browser.