Calculator Input
Example Data Table
| X | Y | Use Case |
|---|---|---|
| 1 | 12.2 | Period 1 demand |
| 2 | 15.1 | Period 2 demand |
| 3 | 18.4 | Period 3 demand |
| 4 | 22.7 | Period 4 demand |
| 5 | 27.9 | Period 5 demand |
| 6 | 34.5 | Period 6 demand |
This sample reflects an approximately exponential pattern, which suits log linear modeling well.
Formula Used
Log linear regression fits a straight line to transformed values rather than raw y values. The core model is ln(y) = a + bx for natural logs, or log10(y) = a + bx for base 10 logs.
The slope is computed with b = Σ[(x - x̄)(ly - lȳ)] / Σ[(x - x̄)²], where ly is the transformed y value. The intercept is a = lȳ - bx̄.
Predictions return to the original scale using ŷ = e^(a + bx) for natural logs or ŷ = 10^(a + bx) for base 10 logs.
Growth per unit x is reported as (exp(b) - 1) × 100% for natural logs, which approximates the percentage change in y for a one unit increase in x.
Confidence intervals here use a normal critical value from the selected confidence level, combined with standard errors from the transformed regression.
How to Use This Calculator
- Enter each x and y observation on its own line.
- Keep every y value above zero so the logarithm exists.
- Select the preferred log base and confidence level.
- Provide an x value for forecasting, if needed.
- Choose the number of decimal places for reporting.
- Click Calculate Regression to display results above the form.
- Review the equation, fit metrics, residuals, and predicted value.
- Use the CSV or PDF buttons to export the output.
Frequently Asked Questions
1. What does log linear regression measure?
It models relationships where y changes multiplicatively while x changes additively. After transforming y with a logarithm, the method estimates a straight-line trend and converts predictions back to the original scale.
2. Why must y values be positive?
A logarithm is undefined for zero and negative values in ordinary real-number regression. Positive y values are required before transformation, coefficient estimation, and prediction can proceed correctly.
3. When should I use natural log instead of base 10?
Natural logs are common in statistics, economics, and growth modeling because coefficient interpretation aligns with continuous percentage change. Base 10 logs can be useful for presentation or domain-specific reporting preferences.
4. How do I interpret the slope?
The slope shows how the transformed response changes when x rises by one unit. Under natural logs, exp(b) - 1 gives the approximate proportional change in y for each additional unit of x.
5. Does a high R² always mean a perfect model?
No. A high R² means the transformed line explains much of the transformed variation, but residual checks, data quality, omitted factors, and forecast stability still matter before trusting the model fully.
6. What are residuals in this calculator?
Residuals are the differences between actual y values and predicted y values on the original scale. They help reveal bias, unusually large errors, and observations that may distort the fitted relationship.
7. Can I use this for forecasting?
Yes. Enter a future or hypothetical x value in the prediction field. The calculator estimates transformed output first, then converts that result back into the original y scale.
8. Is this the same as a log-log model?
No. This page transforms only y, not x. A log-log model transforms both variables and interprets the slope as elasticity. Log linear regression keeps x on its original scale.