Logarithmic Regression Calculator

Fit logarithmic models from paired values accurately. Check slope, intercept, R², residuals, and prediction values. Download reports, inspect graphs, and learn each calculation step.

Calculator

Enter one pair per line. Use commas, spaces, tabs, or semicolons between x and y. Every x value must be positive.

Example Data Table

X	Y
1	2.4
2	3.1
3	3.8
4	4.2
5	4.6
6	4.9
8	5.4
10	5.8

Formula Used

This calculator fits the logarithmic model: y = a + b ln(x)

First, each x value is transformed with the natural logarithm. Then linear least squares estimates the intercept and slope.

Slope:

b = [nΣ(ln(x)y) - Σln(x)Σy] / [nΣ(ln(x))² - (Σln(x))²]

Intercept:

a = ȳ - b · mean(ln(x))

Fit quality is summarized with R squared, adjusted R squared, RMSE, MAE, MAPE, and standard error.

How to Use This Calculator

Enter x and y values as paired rows.
Keep every x value greater than zero.
Set decimal places for cleaner output.
Optionally enter an x value for prediction.
Update chart and axis labels if needed.
Click Run Regression to calculate the model.
Review the equation, fit metrics, table, and graph.
Use the download buttons to save CSV or PDF output.

Frequently Asked Questions

1) What does logarithmic regression measure?

It models relationships where y changes with the logarithm of x. This is useful when growth slows over time, but still rises or falls in a predictable pattern.

2) Why must x be positive?

The natural logarithm is only defined for positive values. Zero and negative x values make ln(x) invalid, so the calculator rejects them.

3) What does the slope mean here?

The slope shows how much y changes when ln(x) increases by one unit. A positive slope means y tends to rise as x grows.

4) How should I interpret R squared?

R squared estimates how much of the y variation is explained by the fitted logarithmic model. Values closer to 1 usually indicate a stronger fit.

5) What is the difference between RMSE and MAE?

RMSE gives more weight to larger errors. MAE treats all absolute errors evenly. Comparing both helps you understand average error size and sensitivity to outliers.

6) Can I predict y for a new x value?

Yes. Enter a positive prediction x value before running the model. The calculator will estimate y using the fitted logarithmic equation.

7) What if all x values are almost identical?

The regression may fail because ln(x) does not vary enough. A useful model needs meaningful spread across the x values.

8) When is logarithmic regression a good choice?

Use it when changes are fast at smaller x values, then gradually level off. Many learning, adoption, and diminishing-return patterns behave like this.