### Question :

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 R^{2} 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.

##
Answer #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.

##
Answer #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/pygrutils.

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.

##
Answer #3:

Looking thru the currently available doc, the closest I’ve been able to determine if this functionality can now be met is if one uses the scipy.stats.pearsonr module.

```
r2 = stats.pearsonr("pct", "rdiff", df)
```

In attempting to make it work directly within a Pandas dataframe, there’s an error kicked out from violating the basic scipy input requirements:

```
TypeError: pearsonr() takes exactly 2 arguments (3 given)
```

I managed to locate another Pandas Seaborn user who evidently solved

it: https://github.com/scipy/scipy/blob/v0.14.0/scipy/stats/stats.py#L2392

```
sns.regplot("rdiff", "pct", df, corr_func=stats.pearsonr);
```

But, unfortunately I haven’t managed to get that to work as it appears the author created his own custom ‘corr_func’ or either there’s an undocumented Seaborn arguement passing method that’s available using a more manual method:

```
# x and y should have same length.
x = np.asarray(x)
y = np.asarray(y)
n = len(x)
mx = x.mean()
my = y.mean()
xm, ym = x-mx, y-my
r_num = np.add.reduce(xm * ym)
r_den = np.sqrt(ss(xm) * ss(ym))
r = r_num / r_den
# Presumably, if abs(r) > 1, then it is only some small artifact of floating
# point arithmetic.
r = max(min(r, 1.0), -1.0)
df = n-2
if abs(r) == 1.0:
prob = 0.0
else:
t_squared = r*r * (df / ((1.0 - r) * (1.0 + r)))
prob = betai(0.5*df, 0.5, df / (df + t_squared))
return r, prob
```

Hope this helps to advance this original request along toward an interim solution as there’s much needed utility to add the regression fitness stats to the Seaborn package as a replacement to what one can easily get from MS-Excel or a stock Matplotlib lineplot.