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 modelâ€™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.

Of course, this was just about validating one assumption â€” 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.

ðŸ‘‰ Over to you: What are some other ways/plots to determine the linear modelâ€™s performance?

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Thank you for this write up Avi Chawla, this is a neat metric to use for assessing the models