Error Prediction Linear Regression Calculator
Analyze regression predictions and residual patterns with confidence. Test data quality using flexible statistical controls. Visual summaries make model errors easier to understand clearly.
Calculator Form
Enter a dataset to fit the line, or switch to manual mode to test an existing model.
Example Data Table
Use this sample dataset to test fitted regression values, residuals, and prediction error metrics.
| Observation | X Value | Y Value |
|---|---|---|
| 1 | 10 | 15.0 |
| 2 | 12 | 18.0 |
| 3 | 14 | 20.0 |
| 4 | 16 | 22.0 |
| 5 | 18 | 25.0 |
| 6 | 20 | 27.0 |
Formula Used
Slope: b1 = Σ[(x - x̄)(y - ȳ)] / Σ[(x - x̄)2]
Intercept: b0 = ȳ - b1x̄
Predicted value: ŷ = b0 + b1x
Residual: e = y - ŷ
MAE: average of absolute residuals
MSE: average of squared residuals
RMSE: √MSE
SEE: √[SSE / (n - 2)]
R²: 1 - SSE / SST
Approximate prediction interval: ŷ ± z × SEE × √[1 + 1/n + (x - x̄)2 / Sxx]
These formulas estimate the line, measure model error, and show how far a future point may reasonably vary from the fitted trend.
How to Use This Calculator
- Select Fit from dataset to estimate the regression line from your X and Y pairs.
- Select Use manual coefficients when you already know the slope and intercept.
- Enter comma, space, or line-separated numbers in both data boxes.
- Add a prediction X value to estimate the corresponding Y output.
- Optionally add an actual Y value to calculate point error metrics.
- Set the interval multiplier. A common value is 1.96.
- Choose decimal places, then press Calculate.
- Review the results, error table, and Plotly charts.
- Download a CSV or PDF copy of the current output.
Frequently Asked Questions
1. What does this calculator measure?
It fits or tests a straight-line model, predicts a Y value from X, and reports error metrics such as residuals, MAE, MSE, RMSE, SEE, and percent error.
2. What is the difference between fit mode and manual mode?
Fit mode estimates slope and intercept from your dataset. Manual mode uses coefficients you provide, which helps when checking an existing model against new observations.
3. Why are residuals important?
Residuals show the gap between actual and predicted values. Their size and pattern reveal bias, outliers, poor fit, or changing variance across the predictor range.
4. What does R squared mean here?
R squared estimates how much variation in Y is explained by the line. Values closer to 1 usually indicate a stronger linear fit, though context still matters.
5. Why can percent error show N/A?
Percent error divides by the actual value. When the actual Y is zero, that division becomes invalid, so the calculator safely reports N/A instead.
6. What is SEE?
SEE stands for standard error of estimate. It summarizes the typical size of residual spread around the fitted line using the squared residual total and sample size.
7. Does the prediction interval guarantee the next point?
No. It is an approximate range based on model assumptions and observed scatter. Real outcomes may still fall outside the interval, especially with weak or noisy data.
8. Can I use this for non-linear relationships?
It is designed for straight-line relationships. If your scatter plot curves strongly, consider transforming the data or using a more suitable non-linear model.