How to get the numerical fitting results when plotting a regression in seaborn?

If I use the seaborn library in Python to plot the result of a linear regression, is there a way to find out the numerical results of the regression? For example, I might want to know the fitting coefficients or the R² of the fit.

I could re-run the same fit using the underlying statsmodels interface, but that would seem to be unnecessary duplicate effort, and anyway I'd want to be able to compare the resulting coefficients to be sure the numerical results are the same as what I'm seeing in the plot.

Solution 1:

There's no way to do this.

In my opinion, asking a visualization library to give you statistical modeling results is backwards. statsmodels, a modeling library, lets you fit a model and then draw a plot that corresponds exactly to the model you fit. If you want that exact correspondence, this order of operations makes more sense to me.

You might say "but the plots in statsmodels don't have as many aesthetic options as seaborn". But I think that makes sense — statsmodels is a modeling library that sometimes uses visualization in the service of modeling. seaborn is a visualization library that sometimes uses modeling in the service of visualization. It is good to specialize, and bad to try to do everything.

Fortunately, both seaborn and statsmodels use tidy data. That means that you really need very little effort duplication to get both plots and models through the appropriate tools.

Solution 2:

Seaborn's creator has unfortunately stated that he won't add such a feature. Below are some options. (The last section contains my original suggestion, which was a hack that used private implementation details of seaborn and was not particularly flexible.)

Simple alternative version of regplot

The following function overlays a fit line on a scatter plot and returns the results from statsmodels. This supports the simplest and perhaps most common usage for sns.regplot, but does not implement any of the fancier functionality.

import statsmodels.api as sm


def simple_regplot(
    x, y, n_std=2, n_pts=100, ax=None, scatter_kws=None, line_kws=None, ci_kws=None
):
    """ Draw a regression line with error interval. """
    ax = plt.gca() if ax is None else ax

    # calculate best-fit line and interval
    x_fit = sm.add_constant(x)
    fit_results = sm.OLS(y, x_fit).fit()

    eval_x = sm.add_constant(np.linspace(np.min(x), np.max(x), n_pts))
    pred = fit_results.get_prediction(eval_x)

    # draw the fit line and error interval
    ci_kws = {} if ci_kws is None else ci_kws
    ax.fill_between(
        eval_x[:, 1],
        pred.predicted_mean - n_std * pred.se_mean,
        pred.predicted_mean + n_std * pred.se_mean,
        alpha=0.5,
        **ci_kws,
    )
    line_kws = {} if line_kws is None else line_kws
    h = ax.plot(eval_x[:, 1], pred.predicted_mean, **line_kws)

    # draw the scatterplot
    scatter_kws = {} if scatter_kws is None else scatter_kws
    ax.scatter(x, y, c=h[0].get_color(), **scatter_kws)

    return fit_results

The results from statsmodels contain a wealth of information, e.g.:

>>> print(fit_results.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                      y   R-squared:                       0.477
Model:                            OLS   Adj. R-squared:                  0.471
Method:                 Least Squares   F-statistic:                     89.23
Date:                Fri, 08 Jan 2021   Prob (F-statistic):           1.93e-15
Time:                        17:56:00   Log-Likelihood:                -137.94
No. Observations:                 100   AIC:                             279.9
Df Residuals:                      98   BIC:                             285.1
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const         -0.1417      0.193     -0.735      0.464      -0.524       0.241
x1             3.1456      0.333      9.446      0.000       2.485       3.806
==============================================================================
Omnibus:                        2.200   Durbin-Watson:                   1.777
Prob(Omnibus):                  0.333   Jarque-Bera (JB):                1.518
Skew:                          -0.002   Prob(JB):                        0.468
Kurtosis:                       2.396   Cond. No.                         4.35
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

A drop-in replacement (almost) for sns.regplot

The advantage of the method above over my original answer below is that it's easy to extend it to more complex fits.

Shameless plug: here is such an extended regplot function that I wrote that implements a large fraction of sns.regplot's functionality: https://github.com/ttesileanu/pydove.

While some features are still missing, the function I wrote

• allows flexibility by separating the plotting from the statistical modeling (and you also get easy access to the fitting results).
• is much faster for large datasets because it lets statsmodels calculate confidence intervals instead of using bootstrapping.
• allows for slightly more diverse fits (e.g., polynomials in log(x)).
• allows for slightly more fine-grained plotting options.

Old answer

Seaborn's creator has unfortunately stated that he won't add such a feature, so here's a workaround.

def regplot(
    *args,
    line_kws=None,
    marker=None,
    scatter_kws=None,
    **kwargs
):
    # this is the class that `sns.regplot` uses
    plotter = sns.regression._RegressionPlotter(*args, **kwargs)

    # this is essentially the code from `sns.regplot`
    ax = kwargs.get("ax", None)
    if ax is None:
        ax = plt.gca()

    scatter_kws = {} if scatter_kws is None else copy.copy(scatter_kws)
    scatter_kws["marker"] = marker
    line_kws = {} if line_kws is None else copy.copy(line_kws)

    plotter.plot(ax, scatter_kws, line_kws)

    # unfortunately the regression results aren't stored, so we rerun
    grid, yhat, err_bands = plotter.fit_regression(plt.gca())

    # also unfortunately, this doesn't return the parameters, so we infer them
    slope = (yhat[-1] - yhat[0]) / (grid[-1] - grid[0])
    intercept = yhat[0] - slope * grid[0]
    return slope, intercept

Note that this only works for linear regression because it simply infers the slope and intercept from the regression results. The nice thing is that it uses seaborn's own regression class and so the results are guaranteed to be consistent with what's shown. The downside is of course that we're using a private implementation detail in seaborn that can break at any point.