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R²: How Much of the Data the Model Actually Explains
When a regression model is built, the immediate question is not only whether the variables are related, but how much of the behaviour in the data the model can actually explain.
That is where R², also known as the coefficient of determination, becomes useful.
It looks at the variation in the dependent variable and asks a straightforward question: how much of that movement can be accounted for by the regression model?
Some of the variation is explained by the independent variable or variables. The rest remains unexplained and sits in the error term. R² simply measures the proportion that the model manages to capture.
Understanding What the Number Means
R² always lies between 0 and 1.
A value close to 0 suggests that the regression model explains very little of what is happening in the dependent variable. Most of the movement is coming from factors outside the model.
A value closer to 1 indicates that the model captures a larger share of the variation.
For example, if a regression produces an R² of 0.60, it means roughly 60 percent of the variation in the dependent variable is explained by the regression, while the remaining 40 percent is influenced by other factors.
In practice, most real-world models fall somewhere between these extremes.
A Helpful Way to Think About It
Imagine observing the returns of a stock over time.
Those returns move up and down for many reasons. Market conditions may explain some of the movement. Firm-specific news may explain another portion. Random fluctuations may explain the rest.
If we run a regression of the stock return on the market return, R² tells us how much of the stock’s movement can be linked to the market factor.
The unexplained portion reflects other influences.
What R² Does Not Tell Us
R² is useful, but it has limits.
A high R² does not mean the regression is necessarily correct. It does not prove causality. And it does not guarantee predictive accuracy.
A model might fit past data well and still perform poorly when used for forecasting.
Because of this, R² should always be interpreted alongside other statistical diagnostics.
Why It Appears Often in Finance
In finance, R² is frequently used when analysing relationships between asset returns and risk factors.
For example, when a stock’s return is regressed on the market return, R² indicates how strongly the stock’s performance is linked to overall market movements.
If R² is low, the stock’s behaviour is largely driven by firm-specific factors rather than the market.
Final Perspective
R² is best understood as a measure of explanatory power. It tells us how much of the variation in the dependent variable the regression model manages to account for.
It does not confirm that the model is correct. It simply shows how much of the data’s behaviour the model can explain.
