Advanced R2 Calculator
Example Data Table
This example shows paired x and y values for a simple fitted line.
| X Value | Observed Y | Use Case |
|---|---|---|
| 1 | 2.1 | Low input level |
| 2 | 3.9 | Early trend check |
| 3 | 6.2 | Middle sample |
| 4 | 7.8 | Model comparison |
| 5 | 10.3 | High input level |
Formula Used
The main coefficient of determination formula is:
R2 = 1 - SSE / SST
SSE = Σ(y - ŷ)²
SST = Σ(y - mean(y))²
For standard simple regression, the fitted value is:
ŷ = intercept + slope × x
The adjusted value is:
Adjusted R2 = 1 - (1 - R2) × (n - 1) / (n - p - 1)
Here, n is row count, and p is predictor count.
How To Use This Calculator
- Choose regression mode or predicted value mode.
- Paste one data pair on each line.
- Select standard intercept or origin based fitting.
- Enter the predictor count for adjusted R2.
- Choose decimal places and residual display.
- Press the calculate button.
- Review R2, adjusted R2, errors, and residuals.
- Export the result as CSV or PDF.
Understanding R2 Statistics
What R2 Means
R2 is called the coefficient of determination. It explains how much variation in the observed values is described by a fitted model. A value near one means the model explains most variation. A value near zero means the model has weak explanatory power. Negative values can occur when predictions are worse than using the mean. That is common with poor external predictions.
Why It Matters
R2 gives a fast view of model fit. It helps compare regression lines, forecasts, and prediction systems. It is useful in statistics, finance, science, engineering, and analytics. Still, it should not be used alone. A high score can hide bias, outliers, or wrong assumptions. Always inspect residuals and error measures too.
Regression And Prediction Modes
This calculator supports two workflows. The first workflow builds a simple linear regression from x and y values. It estimates slope, intercept, fitted values, and residuals. The second workflow accepts predicted and actual values. That mode is useful when predictions came from another model or software.
Adjusted R2
Adjusted R2 adds a penalty for extra predictors. It is helpful when comparing models with different feature counts. A model may gain normal R2 by adding weak variables. Adjusted R2 reduces that reward. This makes it better for model selection.
Reading The Error Values
SSE is the total squared prediction error. MSE is the average squared error. RMSE shows error in the original unit. MAE shows average absolute error. Smaller error values usually mean better predictions. Compare them with the data scale.
Best Practice
Use clean paired data. Remove duplicate headers before pasting values. Check outliers before trusting the final score. Use residual rows to locate weak observations. For serious decisions, combine R2 with plots, domain knowledge, and validation data.
FAQs
1. What is R2 in statistics?
R2 measures how much variation in the actual values is explained by the fitted model. A higher value usually means better fit, but it does not prove the model is correct.
2. Can R2 be negative?
Yes. Negative R2 can happen when model predictions perform worse than simply using the average actual value for every row.
3. What is a good R2 value?
A good value depends on the field. Controlled physical data may need very high R2. Human behavior or market data may have useful models with lower values.
4. What is adjusted R2?
Adjusted R2 modifies R2 by considering sample size and predictor count. It helps compare models that use different numbers of variables.
5. Should I use standard intercept or zero intercept?
Use standard intercept for most regression tasks. Use zero intercept only when theory requires the line to pass through zero.
6. What data format should I paste?
Paste one pair per line. Use commas, spaces, tabs, or pipes between values. The calculator reads the first two numeric values from each row.
7. Is R2 enough to judge a model?
No. R2 should be reviewed with residuals, RMSE, MAE, sample size, and subject knowledge. A high value can still hide poor assumptions.
8. Why use predicted and actual mode?
Use that mode when another tool already generated predictions. Paste predicted values first and actual values second to evaluate model performance.