Why R-squared is a Flawed Regression Metric

...and how to avoid misleading conclusions from it.

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R2 is quite popularly used all across data science and statistics to assess a model.

Yet, contrary to common belief, it is often interpreted as a performance metric for evaluating a model, when, in reality, it is not.

Let’s understand!

R2 tells the fraction of variability in the outcome variable captured by a model.

It is defined as follows:

\(R^2 = \frac{\text{Variability captured by the model}}{\text{Total variability in the data}}\)

In simple words, variability depicts the noise in the outcome variable (y).

Left: The outcome variable has zero variance. Right: The outcome variable has a non-zero variance.

Thus, the more variability captured, the higher the R2.

This means that solely optimizing for R2 as a performance measure:

• promotes 100% overfitting.

• leads us to engineer the model in a way that captures random noise instead of underlying patterns.

It is important to note that:

• R2 is NOT a measure of predictive power.

• Instead, R2 is a fitting measure.

Thus, you should NEVER use it to measure goodness of fit.

This is evident from the image below:

• An overly complex and overfitted model almost gets a perfect R2 of 1.

• A better and more generalized model gets a lower R2 score.

Some other flaws of R2 are:

• R2 always increases as you add more features, even if they are random noise.

• In some cases, one can determine R2 even before fitting a model‌, which is weird.

👉 Read my full blog on the A-Z of R2, what it is, its limitations, and much more here: Flaws of R2 Metric.

👉 Over to you: What are some other flaws in R2?

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I like to explore, experiment and write about data science concepts and tools. You can connect with me on LinkedIn and Twitter.