An Underrated Technique to Visually Assess Linear Regression Performance

Assumption turned into performance validation.

Linear regression assumes that the model residuals (=actual-predicted) are normally distributed.

If the model is underperforming, it may be due to a violation of this assumption.

Here, I often use a residual distribution plot to verify this and determine the model’s performance.

As the name suggests, this plot depicts the distribution of residuals (=actual-predicted), as shown below:

A good residual plot will:

• Follow a normal distribution

• NOT reveal trends in residuals

A bad residual plot will:

• Show skewness

• Reveal patterns in residuals

Thus, the more normally distributed the residual plot looks, the more confident we can be about our model.

This is especially useful when the regression line is difficult to visualize, i.e., in a high-dimensional dataset.

Why?

Because a residual distribution plot depicts the distribution of residuals, which is always one-dimensional.

Thus, it can be plotted and visualized easily.

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Of course, this was just about validating one assumption — the normality of residuals.

However, linear regression relies on many other assumptions, which must be tested as well.

Statsmodel provides a pretty comprehensive report for this:

Read the following issue if you want to learn how to interpret this report:

And if you want to learn where the assumptions originate from, then read this deep dive.

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👉 Over to you: What are some other ways/plots to determine the linear model’s performance?

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