R-squared (R²) is the share of the variation in one number that a regression line explains, from 0 (none) to 1 (all). For a straight line with one predictor it equals the correlation squared.
R² = 1 − Σ (y − ŷ)² ÷ Σ (y − ȳ)² (for one predictor, the square of r)
On the 30-day sample below: 0.52.
When to use it
It tells you how much of the day-to-day movement a single factor accounts for, and so how much is left for everything else.
Worked example
A high R² does not make a model useful, and a low one does not make it useless: a factor that explains a small share of a large number can still be worth a lot.
=RSQ(C2:C31,B2:B31)| Day | Ad spend (₹) | Website orders |
|---|---|---|
| 1 | ₹3,800 | 24 |
| 2 | ₹3,000 | 27 |
| 3 | ₹3,900 | 22 |
| 4 | ₹3,200 | 30 |
| 5 | ₹4,000 | 28 |
| 6 | ₹4,100 | 25 |
| 7 | ₹3,100 | 31 |
| 8 | ₹3,600 | 29 |
| 9 | ₹4,100 | 26 |
| 10 | ₹3,500 | 33 |
| 11 | ₹4,300 | 30 |
| 12 | ₹4,500 | 28 |
| 13 | ₹3,900 | 35 |
| 14 | ₹3,900 | 32 |
| 15 | ₹4,300 | 29 |
| 16 | ₹3,700 | 34 |
| 17 | ₹7,200 | 61 |
| 18 | ₹4,800 | 31 |
| 19 | ₹3,800 | 36 |
| 20 | ₹4,500 | 33 |
| 21 | ₹4,500 | 30 |
| 22 | ₹4,000 | 37 |
| 23 | ₹4,200 | 35 |
| 24 | ₹4,800 | 32 |
| 25 | ₹4,300 | 38 |
| 26 | ₹5,000 | 36 |
| 27 | ₹3,900 | 34 |
| 28 | ₹5,000 | 40 |
| 29 | ₹5,200 | 37 |
| 30 | ₹4,700 | 39 |
Common mistakes
- Adding predictors always raises R²; use adjusted R² when comparing models with different numbers of inputs.
- One extreme point (day 17 here) can produce most of the R².
- R² says nothing about whether the relationship is causal.
Calculate it yourself
Related methods
See all statistics methods or the business metrics they are used on.
Guides that use it
Further reading
Questions people ask
- What is r-squared?
- R-squared (R²) is the share of the variation in one number that a regression line explains, from 0 (none) to 1 (all). For a straight line with one predictor it equals the correlation squared.
- What is the formula for r-squared?
- R² = 1 − Σ (y − ŷ)² ÷ Σ (y − ȳ)² (for one predictor, the square of r). On the 30-day sample data the result is 0.52.
- How do you calculate r-squared in Excel?
- Use =RSQ(C2:C31,B2:B31) with the data in rows 2 to 31. The same formula works in Google Sheets.
About the data on this page
The figures come from a small made-up dataset, printed above in full so you can check every number by hand. Download it as daily.csv. The results are computed from those rows when the page is built, and the Excel formulas, SQL and Python on these pages are run against the same rows before publishing, so the code and the answers agree.
To get these numbers from your own data without writing formulas, try AnalyzeIt: ask in plain words and it shows the working behind every figure.
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