Calculator Inputs
Enter paired values to fit a simple linear regression equation.
Plotly Graph
The scatter points show observations. The line shows the fitted prediction equation.
Example Data Table
Use this sample dataset to test the calculator quickly.
| # | X | Y |
|---|---|---|
| 1 | 1 | 3.1 |
| 2 | 2 | 4.9 |
| 3 | 3 | 7.2 |
| 4 | 4 | 8.8 |
| 5 | 5 | 11.1 |
| 6 | 6 | 12.9 |
| 7 | 7 | 15.4 |
| 8 | 8 | 16.8 |
Formula Used
Simple linear regression equation:
ŷ = b₀ + b₁x
Slope:
b₁ = Σ[(x - x̄)(y - ȳ)] / Σ[(x - x̄)²]
Intercept:
b₀ = ȳ - b₁x̄
Prediction:
ŷ(new) = b₀ + b₁x(new)
Goodness of fit:
R² = 1 - SSE / SST
The calculator fits one straight line through paired observations. It then reports the equation, model accuracy metrics, residual errors, and a prediction for your chosen input.
How to Use This Calculator
- Enter the feature values in the first field.
- Enter matching target values in the second field.
- Add one future input if you want a prediction.
- Choose decimal precision for cleaner output formatting.
- Rename the feature and target labels if needed.
- Press Calculate Regression to generate the equation.
- Review the model metrics, prediction, and residual table.
- Use the export buttons to download result tables as CSV or PDF.
Frequently Asked Questions
1. What does this calculator estimate?
It estimates a simple linear regression equation from paired X and Y values. The page also calculates prediction output, fit strength, residual errors, and several quality metrics.
2. What is the slope in linear regression?
The slope shows how much the predicted target changes when the feature increases by one unit. A positive slope suggests growth, while a negative slope suggests decline.
3. What does the intercept mean?
The intercept is the predicted target value when the feature equals zero. It helps position the regression line, though it may not always have a practical real-world meaning.
4. Why is R² important?
R² measures how much target variation is explained by the fitted line. Higher values usually indicate a better fit, but they do not guarantee causation or perfect future predictions.
5. What are residuals?
Residuals are the differences between actual values and predicted values. They help reveal bias, spread, unusual points, and whether the line misses important patterns in the data.
6. Can I use this for multiple features?
No. This tool fits one predictor and one target only. For several predictors, use multiple linear regression methods that solve several coefficients simultaneously.
7. What causes calculation errors?
Errors usually happen when list lengths differ, values are nonnumeric, or every X value is identical. The model needs valid paired observations and variation in the feature values.
8. When should I trust the prediction?
Predictions are more reliable when data follows a roughly linear trend, residual errors stay moderate, and the new input remains close to the original feature range.