Calculator Input
Example Data Table
This sample shows a positive regression pattern.
| Observation | Study Hours X | Score Y |
|---|---|---|
| 1 | 1 | 2.1 |
| 2 | 2 | 2.9 |
| 3 | 3 | 3.8 |
| 4 | 4 | 5.2 |
| 5 | 5 | 5.9 |
| 6 | 6 | 7.1 |
Formula Used
The percentage of variation explained by a regression model is based on R squared.
Explained Variation % = R² × 100
Unexplained Variation % = 100 − Explained Variation %
R² = SSR / SST
SST = Σ(y − mean y)²
SSE = Σ(y − predicted y)²
SSR = SST − SSE
A higher percentage means the model explains more variation in the response variable. A lower percentage means more variation remains in the residuals.
How to Use This Calculator
- Select raw data if you have X and Y observations.
- Paste one X and Y pair on each line.
- Select summary values if you already know SST, SSR, SSE, or r.
- Set decimal places for cleaner reporting.
- Click Calculate to show results below the header.
- Use CSV or PDF buttons to export your report.
Understanding Percentage of Variation in Regression
What the Value Means
The percentage of variation in regression shows how much movement in Y is explained by X. It converts R squared into a percentage. This makes the result easier to read. A value of 80% means the model explains 80% of the total variation. The remaining 20% is unexplained variation. That part stays inside the residual errors.
Why It Matters
Regression is often used to measure model strength. A model can have a visible trend. Yet the trend may not explain much variation. This calculator helps you judge that difference. It reports R, R squared, SST, SSR, SSE, RMSE, and the F statistic. These outputs help students, analysts, and researchers review model quality.
Explained and Unexplained Parts
Total variation is called SST. Explained variation is called SSR. Error variation is called SSE. The calculator compares SSR with SST. It then multiplies the ratio by 100. This gives the explained variation percentage. The unexplained percentage is the remainder. Both values should usually add to 100%.
Using Raw Data
Raw data mode builds the regression line from X and Y pairs. It finds the slope and intercept. It predicts Y values. It also measures residuals for each row. This is useful when you want a full diagnostic view. The residual table can reveal unusual observations.
Using Summary Inputs
Summary mode is faster when you already know SST and SSR. You can also enter SST with SSE. If you only know correlation r, enter that value. The calculator squares r and converts it into a percentage. This mode is useful for textbook problems and reports.
Reading the Result
A high percentage can suggest a strong fit. It does not prove the model is correct. Always review residuals, context, and data quality. A useful model should be meaningful and stable.
FAQs
1. What is percentage of variation in regression?
It is the share of total Y variation explained by the regression model. It equals R squared multiplied by 100.
2. Is this the same as R squared?
It is R squared expressed as a percentage. For example, R squared of 0.72 becomes 72% explained variation.
3. What does unexplained variation mean?
Unexplained variation is the part of Y variation not explained by the model. It is linked to residual error.
4. Can I use raw X and Y data?
Yes. Enter one X and Y pair per line. The calculator builds the regression line and computes variation values.
5. Can I use summary values only?
Yes. Enter SST with SSR or SSE. You can also enter correlation r to calculate R squared percentage.
6. What is a good explained variation percentage?
It depends on the field and data. Higher is often better, but residual patterns and practical meaning still matter.
7. Why is my result not valid?
Your data may have no variation in X or Y. Regression needs variation to estimate fit and explained percentage.
8. What exports are available?
You can download a CSV summary or a PDF report. Both include the main regression variation results.