How to compute R-squared for a simple linear model (in Python, using SciPy)

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Task

Let’s say we have fit a linear model to two columns of data, one for a single independent variable $x$ and the other for a single dependent variable $y$. How can we compute $R^2$ for that model, to measure its goodness of fit?

Related tasks:

• How to fit a linear model to two columns of data
• How to compute adjusted R-squared

Solution

We assume you have already fit a linear model to the data, as in the code below, which is explained fully in a separate task, how to fit a linear model to two columns of data.

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import scipy.stats as stats
xs = [ 393, 453, 553, 679, 729, 748, 817 ]
ys = [  24,  25,  27,  36,  55,  68,  84 ]
model = stats.linregress( xs, ys )

The $R$ value is part of the model object that stats.linregress returns.

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model.rvalue

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0.8949574425541466

You can compute $R^2$ just by squaring it.

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model.rvalue ** 2

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0.8009488239830586

Content last modified on 24 July 2023.

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Contributed by Nathan Carter (ncarter@bentley.edu)