What it means
Every set of outcomes has variation in it: monthly sales bounce around, so do costs and share prices. A model attempts to explain that bouncing using one or more drivers, and R-squared reports what share of the total variation the model successfully explains.
The mechanics compare two quantities. Total variation measures how far each actual value sits from the simple average of all values, while residual variation measures how far each actual value sits from what the model predicted, so if the model predicts well the residual variation is small and R-squared is close to 1.
In practical finance work R-squared appears in sales forecasting, cost behaviour analysis and portfolio management. When an analyst says a fund has an R-squared of 0.95 against its benchmark index, it means almost all of the fund's movement is explained by the index, which puts any claim of stock-picking skill in perspective.
The most common trap is treating a high R-squared as proof that one thing causes another. Two series that both rise over time will produce a flattering R-squared even when they have nothing to do with each other, so causation has to come from business logic rather than from the statistic.
A second nuance is that adding more explanatory variables can only push R-squared up, never down, which tempts people into stuffing models with drivers. Adjusted R-squared corrects for this by penalising extra variables, and it is the better number to quote when comparing models of different sizes.
In practice
Real-world examples.
Example
A subscription business regresses monthly churn against average support response time and gets an R-squared of 0.31. Support time clearly matters, but 69% of churn variation comes from elsewhere, so the team keeps looking rather than declaring the problem solved.
Example
An index-tracking fund reports an R-squared of 0.99 against its benchmark. The trustees use that number to confirm the fund is doing exactly what it promised, which is to mirror the index rather than beat it.
Example
A manufacturer models overhead cost against machine hours to split fixed from variable costs and obtains an R-squared of 0.88. The cost accountant is comfortable using the fitted line for budgeting, while noting that the remaining 12% needs a separate explanation.
Formula
Calculation
R-squared = 1 - (residual sum of squares / total sum of squares). With a single explanatory variable it is also simply the correlation coefficient squared.
A regional distributor builds a model predicting monthly revenue from the number of active sales representatives. Across 36 months, the total sum of squares, meaning the total squared variation of actual revenue around its own average, is 500,000 (measured in squared thousands of dollars). After fitting the model, the residual sum of squares, the squared variation left unexplained, is 90,000.
R-squared = 1 - (90,000 / 500,000) = 1 - 0.18 = 0.82. So 82% of the month-to-month variation in revenue is explained by headcount, and 18% is driven by everything else, including seasonality, pricing and competitor activity. As a cross-check, because this model has one explanatory variable, the correlation coefficient between headcount and revenue must be the square root of 0.82, roughly 0.91. If instead the correlation had been 0.90, R-squared would be 0.90 x 0.90 = 0.81.Case study
Seen in the real world.
This is an illustrative example featuring a fictional business. Grellow Fitness, a chain of 24 gyms, wanted to know whether its local advertising spend actually drove new memberships. The marketing manager was convinced it did; the finance director was not, because sign-ups also spiked every January regardless of spend.
The analyst regressed monthly new memberships against advertising spend across three years of data and found an R-squared of 0.42. She then added a January indicator and a variable for local competitor openings, and the adjusted R-squared rose to 0.71, while the coefficient on advertising spend shrank sharply. In plain terms, much of what had looked like advertising effect was really seasonality.
Grellow shifted roughly a third of its advertising budget away from January, when sign-ups were coming anyway, into the quieter summer months. In this fictional account the team was careful to describe the model as evidence rather than proof, since a strong statistical relationship still does not establish that one thing causes the other.
Watch out
Common mistakes.
- Reading a high R-squared as proof of cause and effect, when it only measures how closely two sets of movements track each other.
- Comparing models with different numbers of explanatory variables using plain R-squared instead of adjusted R-squared, which unfairly rewards the bigger model.
- Assuming a low R-squared means the model is worthless, when in areas such as individual share returns even a small explained share can be commercially valuable.
Questions
People also ask.
What counts as a good R-squared?
It depends entirely on the field: cost accounting models often exceed 0.90, while models of human or market behaviour may be useful at 0.20 to 0.40.
Is R-squared the same as the correlation coefficient?
Not quite, they are related but different: with one explanatory variable, R-squared is the correlation coefficient squared, so a correlation of 0.90 gives an R-squared of 0.81.
Can R-squared be negative?
Not in ordinary regression, but some out-of-sample versions of the measure can go below zero, which simply means the model predicts worse than using the plain average.
From the founder's library
Take it further with the book.
Build your financial confidence beyond this definition. Shihan's full-length guide, Accounting Fundamentals, takes the same plain-English approach and turns it into a complete, practical playbook for non-finance managers, business owners and students - with chapter-end quiz answers and presentation slides included.
25% off with code MMHQ25, applied at checkout. Priced in USD - checkout may show the equivalent in your local currency.
View the book and save 25%