What it means
Whenever you fit a line or a model to data, you are trying to explain why the outcome moves around. R-squared compares the variation your model failed to explain with the total variation that was there to begin with.
If the model explains most of it, R-squared approaches 1; if the model is no better than simply predicting the average every time, R-squared approaches 0. In business analysis, the statistic turns up wherever someone regresses one series against another.
A marketing team might regress weekly sales against advertising spend, a finance team might regress a fund's returns against a market index, and an operations team might regress delivery times against distance. In each case R-squared answers the same question: how much of the story does this explanation cover?
The most common abuse is treating a high R-squared as proof of causation. Two series that both rise over time will fit each other beautifully without one causing the other, which is why analysts prefer to model changes rather than levels.
A model can also score well simply because it has been given many variables, which is why adjusted R-squared, a version that penalises extra variables, is usually the more honest figure to report. The number that counts as good depends entirely on the field.
Explaining stock returns is hard, and an R-squared of 0.3 may be genuinely useful, whereas a physical process measured with good instruments might be expected to reach 0.98. Judging a marketing model against a physics standard is a mistake, and so is celebrating a fit that is normal for the domain.
In investing, R-squared has a specific and practical use: it shows how closely a fund tracks its benchmark. An index tracker should show an R-squared close to 1 against its index, and if an actively managed fund charging active fees shows 0.97, the investor is paying for a portfolio that behaves almost exactly like the cheap index alternative.
That single check has saved a lot of investors a lot of money.
In practice
Real-world examples.
Example
A subscription business regresses monthly churn against average support response time and gets an R-squared of 0.22. The relationship is real but weak, so the team reports it as one contributing factor rather than the explanation for churn.
Example
An investor compares two equity funds against the same index. The first shows an R-squared of 0.99 and charges 0.85% a year; the second shows 0.62 and charges the same, and the investor concludes only the second is doing anything an index fund could not.
Example
A logistics analyst models delivery time against distance and gets an R-squared of 0.71. Adding traffic density and time of day lifts it to 0.88, and the adjusted figure confirms the improvement is not just a product of adding more variables.
Think of it
“R-squared shows how much returns track the benchmark-correlation to reference.
Formula
Calculation
R-squared = 1 - (unexplained variation / total variation), where unexplained variation is the sum of squared differences between actual and predicted values, and total variation is the sum of squared differences between actual values and their average.
A retailer models monthly sales against advertising spend across three years of data. The total variation in monthly sales, measured as the sum of squared deviations from the mean, comes to 4,000 units. After fitting the model, the sum of the squared errors between predicted and actual sales is 600 units.
R-squared = 1 - (600 / 4,000) = 1 - 0.15 = 0.85. So 85% of the month-to-month variation in sales is explained by advertising spend, and 15% is left to seasonality, competitor activity, weather and noise. As a cross-check, R-squared is the square of the correlation between the two series, so a correlation of 0.92 would give 0.92 x 0.92 = 0.8464, or roughly 85%.Case study
Seen in the real world.
Bramblewood Foods is an illustrative, invented snack manufacturer whose marketing director built a model regressing quarterly revenue against television advertising spend. The model returned an R-squared of 0.94, and the director used it to argue for a 40% increase in the advertising budget.
The finance team looked more closely. Both revenue and advertising spend had grown steadily every quarter for five years, so the model was largely measuring a shared upward trend rather than a response. When the analysis was rerun on quarter-on-quarter changes rather than levels, the R-squared fell to 0.19, and the apparent relationship mostly disappeared.
In this fictional case the company ran a regional holdout test instead, cutting advertising in two comparable regions and comparing results. That experiment found a genuine but much smaller effect, and the budget increase that eventually got approved was a third of the size originally proposed. The illustrative lesson is that a high R-squared measures fit, and fit is not evidence.
Watch out
Common mistakes.
- Reading a high R-squared as proof that one variable causes the other. Correlated trends produce excellent fits all the time, and only an experiment or careful design can establish causation.
- Comparing R-squared across models with different outcome variables. The statistic is only comparable between models predicting the same thing on the same data.
- Adding variables until R-squared looks impressive. R-squared never falls when you add a variable, which is why adjusted R-squared exists and why holding back test data matters.
Questions
People also ask.
What is a good R-squared?
It depends entirely on the field, since 0.3 can be valuable in financial returns while 0.9 might be poor for a well-instrumented physical process.
What is the difference between R-squared and adjusted R-squared?
Adjusted R-squared applies a penalty for each additional variable, so it can fall when you add something useless, which makes it the fairer figure for comparing models.
Can R-squared be negative?
Not in a standard regression with an intercept, but it can go negative when a fitted model is applied to new data and performs worse than simply predicting the average.
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