Section 4.4 — Regression with categorical predictors#
This notebook contains the code examples from Section 4.4 Regression with categorical predictors from the No Bullshit Guide to Statistics.
Notebook setup#
# load Python modules
import os
import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
# Figures setup
plt.clf() # needed otherwise `sns.set_theme` doesn't work
from plot_helpers import RCPARAMS
# RCPARAMS.update({'figure.figsize': (10, 3)}) # good for screen
RCPARAMS.update({'figure.figsize': (5, 1.6)}) # good for print
sns.set_theme(
context="paper",
style="whitegrid",
palette="colorblind",
rc=RCPARAMS,
)
# High-resolution please
%config InlineBackend.figure_format = 'retina'
# Where to store figures
DESTDIR = "figures/lm/categorical"
<Figure size 640x480 with 0 Axes>
#######################################################
Definitions#
import pandas as pd
import statsmodels.formula.api as smf
Design matrix for linear model lm1#
students = pd.read_csv("../datasets/students.csv")
lm1 = smf.ols("score ~ 1 + effort", data=students).fit()
lm1.model.exog[0:3]
array([[ 1. , 10.96],
[ 1. , 8.69],
[ 1. , 8.6 ]])
students["effort"].values[0:3]
array([10.96, 8.69, 8.6 ])
Design matrix for linear model lm2#
doctors = pd.read_csv("../datasets/doctors.csv")
formula = "score ~ 1 + alc + weed + exrc"
lm2 = smf.ols(formula, data=doctors).fit()
lm2.model.exog[0:3]
array([[ 1. , 0. , 5. , 0. ],
[ 1. , 20. , 0. , 4.5],
[ 1. , 1. , 0. , 7. ]])
doctors[["alc","weed","exrc"]].values[0:3]
array([[ 0. , 5. , 0. ],
[20. , 0. , 4.5],
[ 1. , 0. , 7. ]])
Example 1: binary predictor variable#
import statsmodels.formula.api as smf
lmloc = smf.ols("score ~ 1 + C(loc)", data=doctors).fit()
lmloc.params
Intercept 52.956522
C(loc)[T.urb] -6.992885
dtype: float64
rur_mean = doctors[doctors["loc"]=="rur"]["score"].mean()
urb_mean = doctors[doctors["loc"]=="urb"]["score"].mean()
rur_mean, urb_mean, urb_mean - rur_mean
(52.95652173913044, 45.96363636363636, -6.992885375494076)
Encoding#
doctors["loc"][0:5]
0 rur
1 urb
2 urb
3 urb
4 rur
Name: loc, dtype: object
lmloc.model.exog[0:5]
array([[1., 0.],
[1., 1.],
[1., 1.],
[1., 1.],
[1., 0.]])
# ALT.
# dmatrix("1 + C(loc)", doctors)[0:5]
Dummy coding for categorical predictors#
cats = ["A", "B", "C", "C"]
catdf = pd.DataFrame({"cat":cats})
catdf
| cat | |
|---|---|
| 0 | A |
| 1 | B |
| 2 | C |
| 3 | C |
from patsy import dmatrix
dmatrix("1 + C(cat)", data=catdf)
DesignMatrix with shape (4, 3)
Intercept C(cat)[T.B] C(cat)[T.C]
1 0 0
1 1 0
1 0 1
1 0 1
Terms:
'Intercept' (column 0)
'C(cat)' (columns 1:3)
Example 2: predictors with three levels#
doctors = pd.read_csv("../datasets/doctors.csv")
doctors["work"].head(5)
0 hos
1 cli
2 hos
3 eld
4 cli
Name: work, dtype: object
dmatrix("1 + C(work)", data=doctors)[0:5]
array([[1., 0., 1.],
[1., 0., 0.],
[1., 0., 1.],
[1., 1., 0.],
[1., 0., 0.]])
lmw = smf.ols("score ~ 1 + C(work)", data=doctors).fit()
lmw.params
Intercept 46.545455
C(work)[T.eld] 4.569930
C(work)[T.hos] 2.668831
dtype: float64
lmw.rsquared
0.0077217625749193
lmw.fvalue, lmw.f_pvalue
(0.5953116925291129, 0.5526627461285702)
Example 3: improved model for the sleep scores#
We can mix of numerical and categorical predictors
formula3 = "score ~ 1 + alc + weed + exrc + C(loc)"
lm3 = smf.ols(formula3, data=doctors).fit()
lm3.params
Intercept 63.606961
C(loc)[T.urb] -5.002404
alc -1.784915
weed -0.840668
exrc 1.783107
dtype: float64
lm3.rsquared, lm3.aic
(0.8544615790287665, 1092.5985552344712)
from ministats import plot_partreg
plot_partreg(lm3, "alc");
WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.
lm3.summary()
| Dep. Variable: | score | R-squared: | 0.854 |
|---|---|---|---|
| Model: | OLS | Adj. R-squared: | 0.851 |
| Method: | Least Squares | F-statistic: | 221.6 |
| Date: | Thu, 19 Dec 2024 | Prob (F-statistic): | 4.18e-62 |
| Time: | 16:25:47 | Log-Likelihood: | -541.30 |
| No. Observations: | 156 | AIC: | 1093. |
| Df Residuals: | 151 | BIC: | 1108. |
| Df Model: | 4 | ||
| Covariance Type: | nonrobust |
| coef | std err | t | P>|t| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| Intercept | 63.6070 | 1.524 | 41.734 | 0.000 | 60.596 | 66.618 |
| C(loc)[T.urb] | -5.0024 | 1.401 | -3.572 | 0.000 | -7.770 | -2.235 |
| alc | -1.7849 | 0.068 | -26.424 | 0.000 | -1.918 | -1.651 |
| weed | -0.8407 | 0.462 | -1.821 | 0.071 | -1.753 | 0.071 |
| exrc | 1.7831 | 0.133 | 13.400 | 0.000 | 1.520 | 2.046 |
| Omnibus: | 4.325 | Durbin-Watson: | 1.823 |
|---|---|---|---|
| Prob(Omnibus): | 0.115 | Jarque-Bera (JB): | 4.038 |
| Skew: | 0.279 | Prob(JB): | 0.133 |
| Kurtosis: | 3.556 | Cond. No. | 46.2 |
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
Compare to the model without loc predictor#
formula2 = "score ~ 1 + alc + weed + exrc"
lm2 = smf.ols(formula2, data=doctors).fit()
F, p, _ = lm3.compare_f_test(lm2)
F, p
(12.758115596295623, 0.0004759812308491827)
Everything is a linear model#
One-sample t-test as a linear model#
kombucha = pd.read_csv("../datasets/kombucha.csv")
ksample04 = kombucha[kombucha["batch"]==4]["volume"]
ksample04.mean()
1003.8335
from scipy.stats import ttest_1samp
resk = ttest_1samp(ksample04, popmean=1000)
resk.statistic, resk.pvalue
(3.087703149420272, 0.0037056653503329618)
# # ALT. using the helper function from `ministats`
# from ministats import ttest_mean
# ttest_mean(ksample04, mu0=1000)
# Prepare zero-centered data (volume - 1000)
kdat04 = pd.DataFrame()
kdat04["zcvolume"] = ksample04 - 1000
# Fit linear model with only an intercept term
import statsmodels.formula.api as smf
lmk = smf.ols("zcvolume ~ 1", data=kdat04).fit()
lmk.params
Intercept 3.8335
dtype: float64
lmk.tvalues.iloc[0], lmk.pvalues.iloc[0]
(3.0877031494203044, 0.0037056653503326335)
Two-sample t-test as a linear model#
East vs. West electricity prices#
eprices = pd.read_csv("../datasets/eprices.csv")
pricesW = eprices[eprices["loc"]=="West"]["price"]
pricesE = eprices[eprices["loc"]=="East"]["price"]
pricesW.mean() - pricesE.mean()
3.000000000000001
Two-sample t-test with pooled variance#
from scipy.stats import ttest_ind
rese = ttest_ind(pricesW, pricesE, equal_var=True)
rese.statistic, rese.pvalue
(5.022875513276465, 0.00012497067987678488)
ci_Delta = rese.confidence_interval(confidence_level=0.9)
[ci_Delta.low, ci_Delta.high]
[1.957240525873166, 4.042759474126836]
Linear model approach#
lme = smf.ols("price ~ 1 + C(loc)", data=eprices).fit()
print(lme.params)
lme.tvalues.iloc[1], lme.pvalues.iloc[1]
Intercept 6.155556
C(loc)[T.West] 3.000000
dtype: float64
(5.02287551327646, 0.00012497067987678602)
lme.conf_int(alpha=0.1).iloc[1].values
array([1.95724053, 4.04275947])
Example 1 (revisited): urban vs. rural doctors#
from scipy.stats import ttest_ind
scoresR = doctors[doctors["loc"]=="rur"]["score"]
scoresU = doctors[doctors["loc"]=="urb"]["score"]
resloc = ttest_ind(scoresU, scoresR, equal_var=True)
resloc.statistic, resloc.pvalue
(-1.9657612140164198, 0.05112460353979369)
lmloc = smf.ols("score ~ 1 + C(loc)", data=doctors).fit()
lmloc.tvalues.iloc[1], lmloc.pvalues.iloc[1]
(-1.9657612140164218, 0.051124603539793465)
One-way ANOVA as a linear model#
from scipy.stats import f_oneway
scoresH = doctors[doctors["work"]=="hos"]["score"]
scoresC = doctors[doctors["work"]=="cli"]["score"]
scoresE = doctors[doctors["work"]=="eld"]["score"]
resw = f_oneway(scoresH, scoresC, scoresE)
resw.statistic, resw.pvalue
(0.5953116925291182, 0.5526627461285608)
lmw = smf.ols("score ~ 1 + C(work)", data=doctors).fit()
print(lmw.params)
lmw.fvalue, lmw.f_pvalue
Intercept 46.545455
C(work)[T.eld] 4.569930
C(work)[T.hos] 2.668831
dtype: float64
(0.5953116925291129, 0.5526627461285702)
from ministats.plots.figures import plot_lm_anova
with plt.rc_context({"figure.figsize":(5,3), "text.usetex":True}):
ax = plot_lm_anova(doctors, x="work", y="score")
ax.set_ylim([31,69])
sns.move_legend(ax, "lower right")
Error in callback <function _draw_all_if_interactive at 0x7fdbe0cb3d90> (for post_execute), with arguments args (),kwargs {}:
---------------------------------------------------------------------------
FileNotFoundError Traceback (most recent call last)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/texmanager.py:247, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
246 try:
--> 247 report = subprocess.check_output(
248 command, cwd=cwd if cwd is not None else cls._texcache,
249 stderr=subprocess.STDOUT)
250 except FileNotFoundError as exc:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/subprocess.py:421, in check_output(timeout, *popenargs, **kwargs)
419 kwargs['input'] = empty
--> 421 return run(*popenargs, stdout=PIPE, timeout=timeout, check=True,
422 **kwargs).stdout
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/subprocess.py:503, in run(input, capture_output, timeout, check, *popenargs, **kwargs)
501 kwargs['stderr'] = PIPE
--> 503 with Popen(*popenargs, **kwargs) as process:
504 try:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/subprocess.py:971, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize)
968 self.stderr = io.TextIOWrapper(self.stderr,
969 encoding=encoding, errors=errors)
--> 971 self._execute_child(args, executable, preexec_fn, close_fds,
972 pass_fds, cwd, env,
973 startupinfo, creationflags, shell,
974 p2cread, p2cwrite,
975 c2pread, c2pwrite,
976 errread, errwrite,
977 restore_signals,
978 gid, gids, uid, umask,
979 start_new_session)
980 except:
981 # Cleanup if the child failed starting.
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/subprocess.py:1863, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session)
1862 err_msg = os.strerror(errno_num)
-> 1863 raise child_exception_type(errno_num, err_msg, err_filename)
1864 raise child_exception_type(err_msg)
FileNotFoundError: [Errno 2] No such file or directory: 'latex'
The above exception was the direct cause of the following exception:
RuntimeError Traceback (most recent call last)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/pyplot.py:279, in _draw_all_if_interactive()
277 def _draw_all_if_interactive() -> None:
278 if matplotlib.is_interactive():
--> 279 draw_all()
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/_pylab_helpers.py:131, in Gcf.draw_all(cls, force)
129 for manager in cls.get_all_fig_managers():
130 if force or manager.canvas.figure.stale:
--> 131 manager.canvas.draw_idle()
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/backend_bases.py:1891, in FigureCanvasBase.draw_idle(self, *args, **kwargs)
1889 if not self._is_idle_drawing:
1890 with self._idle_draw_cntx():
-> 1891 self.draw(*args, **kwargs)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/backends/backend_agg.py:382, in FigureCanvasAgg.draw(self)
379 # Acquire a lock on the shared font cache.
380 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
381 else nullcontext()):
--> 382 self.figure.draw(self.renderer)
383 # A GUI class may be need to update a window using this draw, so
384 # don't forget to call the superclass.
385 super().draw()
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/artist.py:94, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
92 @wraps(draw)
93 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 94 result = draw(artist, renderer, *args, **kwargs)
95 if renderer._rasterizing:
96 renderer.stop_rasterizing()
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/artist.py:71, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
68 if artist.get_agg_filter() is not None:
69 renderer.start_filter()
---> 71 return draw(artist, renderer)
72 finally:
73 if artist.get_agg_filter() is not None:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/figure.py:3257, in Figure.draw(self, renderer)
3254 # ValueError can occur when resizing a window.
3256 self.patch.draw(renderer)
-> 3257 mimage._draw_list_compositing_images(
3258 renderer, self, artists, self.suppressComposite)
3260 renderer.close_group('figure')
3261 finally:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/image.py:134, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
132 if not_composite or not has_images:
133 for a in artists:
--> 134 a.draw(renderer)
135 else:
136 # Composite any adjacent images together
137 image_group = []
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/artist.py:71, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
68 if artist.get_agg_filter() is not None:
69 renderer.start_filter()
---> 71 return draw(artist, renderer)
72 finally:
73 if artist.get_agg_filter() is not None:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/axes/_base.py:3181, in _AxesBase.draw(self, renderer)
3178 if artists_rasterized:
3179 _draw_rasterized(self.get_figure(root=True), artists_rasterized, renderer)
-> 3181 mimage._draw_list_compositing_images(
3182 renderer, self, artists, self.get_figure(root=True).suppressComposite)
3184 renderer.close_group('axes')
3185 self.stale = False
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/image.py:134, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
132 if not_composite or not has_images:
133 for a in artists:
--> 134 a.draw(renderer)
135 else:
136 # Composite any adjacent images together
137 image_group = []
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/artist.py:71, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
68 if artist.get_agg_filter() is not None:
69 renderer.start_filter()
---> 71 return draw(artist, renderer)
72 finally:
73 if artist.get_agg_filter() is not None:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/axis.py:1416, in Axis.draw(self, renderer)
1413 renderer.open_group(__name__, gid=self.get_gid())
1415 ticks_to_draw = self._update_ticks()
-> 1416 tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)
1418 for tick in ticks_to_draw:
1419 tick.draw(renderer)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/axis.py:1343, in Axis._get_ticklabel_bboxes(self, ticks, renderer)
1341 if renderer is None:
1342 renderer = self.get_figure(root=True)._get_renderer()
-> 1343 return ([tick.label1.get_window_extent(renderer)
1344 for tick in ticks if tick.label1.get_visible()],
1345 [tick.label2.get_window_extent(renderer)
1346 for tick in ticks if tick.label2.get_visible()])
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/axis.py:1343, in <listcomp>(.0)
1341 if renderer is None:
1342 renderer = self.get_figure(root=True)._get_renderer()
-> 1343 return ([tick.label1.get_window_extent(renderer)
1344 for tick in ticks if tick.label1.get_visible()],
1345 [tick.label2.get_window_extent(renderer)
1346 for tick in ticks if tick.label2.get_visible()])
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/text.py:969, in Text.get_window_extent(self, renderer, dpi)
964 raise RuntimeError(
965 "Cannot get window extent of text w/o renderer. You likely "
966 "want to call 'figure.draw_without_rendering()' first.")
968 with cbook._setattr_cm(fig, dpi=dpi):
--> 969 bbox, info, descent = self._get_layout(self._renderer)
970 x, y = self.get_unitless_position()
971 x, y = self.get_transform().transform((x, y))
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
370 ys = []
372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
374 renderer, "lp", self._fontproperties,
375 ismath="TeX" if self.get_usetex() else False,
376 dpi=self.get_figure(root=True).dpi)
377 min_dy = (lp_h - lp_d) * self._linespacing
379 for i, line in enumerate(lines):
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
67 # Cached based on a copy of fontprop so that later in-place mutations of
68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
70 weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
73 @functools.lru_cache(4096)
74 def _get_text_metrics_with_cache_impl(
75 renderer_ref, text, fontprop, ismath, dpi):
76 # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77 return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/backends/backend_agg.py:211, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
209 _api.check_in_list(["TeX", True, False], ismath=ismath)
210 if ismath == "TeX":
--> 211 return super().get_text_width_height_descent(s, prop, ismath)
213 if ismath:
214 ox, oy, width, height, descent, font_image = \
215 self.mathtext_parser.parse(s, self.dpi, prop)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/backend_bases.py:566, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
562 fontsize = prop.get_size_in_points()
564 if ismath == 'TeX':
565 # todo: handle properties
--> 566 return self.get_texmanager().get_text_width_height_descent(
567 s, fontsize, renderer=self)
569 dpi = self.points_to_pixels(72)
570 if ismath:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/texmanager.py:360, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
358 if tex.strip() == '':
359 return 0, 0, 0
--> 360 dvifile = cls.make_dvi(tex, fontsize)
361 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
362 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/texmanager.py:292, in TexManager.make_dvi(cls, tex, fontsize)
290 with TemporaryDirectory(dir=cwd) as tmpdir:
291 tmppath = Path(tmpdir)
--> 292 cls._run_checked_subprocess(
293 ["latex", "-interaction=nonstopmode", "--halt-on-error",
294 f"--output-directory={tmppath.name}",
295 f"{texfile.name}"], tex, cwd=cwd)
296 (tmppath / Path(dvifile).name).replace(dvifile)
297 return dvifile
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/texmanager.py:251, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
247 report = subprocess.check_output(
248 command, cwd=cwd if cwd is not None else cls._texcache,
249 stderr=subprocess.STDOUT)
250 except FileNotFoundError as exc:
--> 251 raise RuntimeError(
252 f'Failed to process string with tex because {command[0]} '
253 'could not be found') from exc
254 except subprocess.CalledProcessError as exc:
255 raise RuntimeError(
256 '{prog} was not able to process the following string:\n'
257 '{tex!r}\n\n'
(...)
264 exc=exc.output.decode('utf-8', 'backslashreplace'))
265 ) from None
RuntimeError: Failed to process string with tex because latex could not be found
---------------------------------------------------------------------------
FileNotFoundError Traceback (most recent call last)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/texmanager.py:247, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
246 try:
--> 247 report = subprocess.check_output(
248 command, cwd=cwd if cwd is not None else cls._texcache,
249 stderr=subprocess.STDOUT)
250 except FileNotFoundError as exc:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/subprocess.py:421, in check_output(timeout, *popenargs, **kwargs)
419 kwargs['input'] = empty
--> 421 return run(*popenargs, stdout=PIPE, timeout=timeout, check=True,
422 **kwargs).stdout
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/subprocess.py:503, in run(input, capture_output, timeout, check, *popenargs, **kwargs)
501 kwargs['stderr'] = PIPE
--> 503 with Popen(*popenargs, **kwargs) as process:
504 try:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/subprocess.py:971, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize)
968 self.stderr = io.TextIOWrapper(self.stderr,
969 encoding=encoding, errors=errors)
--> 971 self._execute_child(args, executable, preexec_fn, close_fds,
972 pass_fds, cwd, env,
973 startupinfo, creationflags, shell,
974 p2cread, p2cwrite,
975 c2pread, c2pwrite,
976 errread, errwrite,
977 restore_signals,
978 gid, gids, uid, umask,
979 start_new_session)
980 except:
981 # Cleanup if the child failed starting.
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/subprocess.py:1863, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session)
1862 err_msg = os.strerror(errno_num)
-> 1863 raise child_exception_type(errno_num, err_msg, err_filename)
1864 raise child_exception_type(err_msg)
FileNotFoundError: [Errno 2] No such file or directory: 'latex'
The above exception was the direct cause of the following exception:
RuntimeError Traceback (most recent call last)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/IPython/core/formatters.py:402, in BaseFormatter.__call__(self, obj)
400 pass
401 else:
--> 402 return printer(obj)
403 # Finally look for special method names
404 method = get_real_method(obj, self.print_method)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/IPython/core/pylabtools.py:187, in retina_figure(fig, base64, **kwargs)
178 def retina_figure(fig, base64=False, **kwargs):
179 """format a figure as a pixel-doubled (retina) PNG
180
181 If `base64` is True, return base64-encoded str instead of raw bytes
(...)
185 base64 argument
186 """
--> 187 pngdata = print_figure(fig, fmt="retina", base64=False, **kwargs)
188 # Make sure that retina_figure acts just like print_figure and returns
189 # None when the figure is empty.
190 if pngdata is None:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/IPython/core/pylabtools.py:170, in print_figure(fig, fmt, bbox_inches, base64, **kwargs)
167 from matplotlib.backend_bases import FigureCanvasBase
168 FigureCanvasBase(fig)
--> 170 fig.canvas.print_figure(bytes_io, **kw)
171 data = bytes_io.getvalue()
172 if fmt == 'svg':
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/backend_bases.py:2155, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
2152 # we do this instead of `self.figure.draw_without_rendering`
2153 # so that we can inject the orientation
2154 with getattr(renderer, "_draw_disabled", nullcontext)():
-> 2155 self.figure.draw(renderer)
2156 if bbox_inches:
2157 if bbox_inches == "tight":
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/artist.py:94, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
92 @wraps(draw)
93 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 94 result = draw(artist, renderer, *args, **kwargs)
95 if renderer._rasterizing:
96 renderer.stop_rasterizing()
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/artist.py:71, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
68 if artist.get_agg_filter() is not None:
69 renderer.start_filter()
---> 71 return draw(artist, renderer)
72 finally:
73 if artist.get_agg_filter() is not None:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/figure.py:3257, in Figure.draw(self, renderer)
3254 # ValueError can occur when resizing a window.
3256 self.patch.draw(renderer)
-> 3257 mimage._draw_list_compositing_images(
3258 renderer, self, artists, self.suppressComposite)
3260 renderer.close_group('figure')
3261 finally:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/image.py:134, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
132 if not_composite or not has_images:
133 for a in artists:
--> 134 a.draw(renderer)
135 else:
136 # Composite any adjacent images together
137 image_group = []
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/artist.py:71, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
68 if artist.get_agg_filter() is not None:
69 renderer.start_filter()
---> 71 return draw(artist, renderer)
72 finally:
73 if artist.get_agg_filter() is not None:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/axes/_base.py:3181, in _AxesBase.draw(self, renderer)
3178 if artists_rasterized:
3179 _draw_rasterized(self.get_figure(root=True), artists_rasterized, renderer)
-> 3181 mimage._draw_list_compositing_images(
3182 renderer, self, artists, self.get_figure(root=True).suppressComposite)
3184 renderer.close_group('axes')
3185 self.stale = False
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/image.py:134, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
132 if not_composite or not has_images:
133 for a in artists:
--> 134 a.draw(renderer)
135 else:
136 # Composite any adjacent images together
137 image_group = []
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/artist.py:71, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
68 if artist.get_agg_filter() is not None:
69 renderer.start_filter()
---> 71 return draw(artist, renderer)
72 finally:
73 if artist.get_agg_filter() is not None:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/axis.py:1416, in Axis.draw(self, renderer)
1413 renderer.open_group(__name__, gid=self.get_gid())
1415 ticks_to_draw = self._update_ticks()
-> 1416 tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)
1418 for tick in ticks_to_draw:
1419 tick.draw(renderer)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/axis.py:1343, in Axis._get_ticklabel_bboxes(self, ticks, renderer)
1341 if renderer is None:
1342 renderer = self.get_figure(root=True)._get_renderer()
-> 1343 return ([tick.label1.get_window_extent(renderer)
1344 for tick in ticks if tick.label1.get_visible()],
1345 [tick.label2.get_window_extent(renderer)
1346 for tick in ticks if tick.label2.get_visible()])
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/axis.py:1343, in <listcomp>(.0)
1341 if renderer is None:
1342 renderer = self.get_figure(root=True)._get_renderer()
-> 1343 return ([tick.label1.get_window_extent(renderer)
1344 for tick in ticks if tick.label1.get_visible()],
1345 [tick.label2.get_window_extent(renderer)
1346 for tick in ticks if tick.label2.get_visible()])
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/text.py:969, in Text.get_window_extent(self, renderer, dpi)
964 raise RuntimeError(
965 "Cannot get window extent of text w/o renderer. You likely "
966 "want to call 'figure.draw_without_rendering()' first.")
968 with cbook._setattr_cm(fig, dpi=dpi):
--> 969 bbox, info, descent = self._get_layout(self._renderer)
970 x, y = self.get_unitless_position()
971 x, y = self.get_transform().transform((x, y))
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
370 ys = []
372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
374 renderer, "lp", self._fontproperties,
375 ismath="TeX" if self.get_usetex() else False,
376 dpi=self.get_figure(root=True).dpi)
377 min_dy = (lp_h - lp_d) * self._linespacing
379 for i, line in enumerate(lines):
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
67 # Cached based on a copy of fontprop so that later in-place mutations of
68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
70 weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
73 @functools.lru_cache(4096)
74 def _get_text_metrics_with_cache_impl(
75 renderer_ref, text, fontprop, ismath, dpi):
76 # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77 return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/backends/backend_agg.py:211, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
209 _api.check_in_list(["TeX", True, False], ismath=ismath)
210 if ismath == "TeX":
--> 211 return super().get_text_width_height_descent(s, prop, ismath)
213 if ismath:
214 ox, oy, width, height, descent, font_image = \
215 self.mathtext_parser.parse(s, self.dpi, prop)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/backend_bases.py:566, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
562 fontsize = prop.get_size_in_points()
564 if ismath == 'TeX':
565 # todo: handle properties
--> 566 return self.get_texmanager().get_text_width_height_descent(
567 s, fontsize, renderer=self)
569 dpi = self.points_to_pixels(72)
570 if ismath:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/texmanager.py:360, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
358 if tex.strip() == '':
359 return 0, 0, 0
--> 360 dvifile = cls.make_dvi(tex, fontsize)
361 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
362 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/texmanager.py:292, in TexManager.make_dvi(cls, tex, fontsize)
290 with TemporaryDirectory(dir=cwd) as tmpdir:
291 tmppath = Path(tmpdir)
--> 292 cls._run_checked_subprocess(
293 ["latex", "-interaction=nonstopmode", "--halt-on-error",
294 f"--output-directory={tmppath.name}",
295 f"{texfile.name}"], tex, cwd=cwd)
296 (tmppath / Path(dvifile).name).replace(dvifile)
297 return dvifile
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/texmanager.py:251, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
247 report = subprocess.check_output(
248 command, cwd=cwd if cwd is not None else cls._texcache,
249 stderr=subprocess.STDOUT)
250 except FileNotFoundError as exc:
--> 251 raise RuntimeError(
252 f'Failed to process string with tex because {command[0]} '
253 'could not be found') from exc
254 except subprocess.CalledProcessError as exc:
255 raise RuntimeError(
256 '{prog} was not able to process the following string:\n'
257 '{tex!r}\n\n'
(...)
264 exc=exc.output.decode('utf-8', 'backslashreplace'))
265 ) from None
RuntimeError: Failed to process string with tex because latex could not be found
<Figure size 500x300 with 1 Axes>
# BONUS: print ANOVA table
# import statsmodels.api as sm
# sm.stats.anova_lm(lmw)
Nonparametric tests#
One-sample Wilcoxon signed-rank test#
kombucha = pd.read_csv("../datasets/kombucha.csv")
ksample04 = kombucha[kombucha["batch"]==4]["volume"]
# Zero-centered volumes
zcksample04 = ksample04 - 1000
from scipy.stats import wilcoxon
reswil = wilcoxon(zcksample04)
reswil.pvalue
0.002770629538645153
# Create a new data frame with the signed ranks of the volumes
df_zcsr = pd.DataFrame()
df_zcsr["zcvolume_sr"] = np.sign(zcksample04) * zcksample04.abs().rank()
lmwil = smf.ols("zcvolume_sr ~ 1", data=df_zcsr).fit()
lmwil.pvalues.iloc[0]
0.0022841508459744237
Mann-Whitney U-test#
scoresR = doctors[doctors["loc"]=="rur"]["score"]
scoresU = doctors[doctors["loc"]=="urb"]["score"]
from scipy.stats import mannwhitneyu
resmwu = mannwhitneyu(scoresU, scoresR)
resmwu.pvalue
0.050083369850737636
# Compute the (unsigned) ranks of the scores
doctors["score_r"] = doctors["score"].rank()
# Fit a linear model
lmmwu = smf.ols("score_r ~ 1 + C(loc)", data=doctors).fit()
lmmwu.pvalues.iloc[1]
0.049533887469988734
Kruskal-Wallis analysis of variance by ranks#
from scipy.stats import kruskal
reskw = kruskal(scoresH, scoresC, scoresE)
reskw.pvalue
0.4441051932875236
# Compute the (unsigned) ranks of the scores
doctors["score_r"] = doctors["score"].rank()
lmkw = smf.ols("score_r ~ 1 + C(work)", data=doctors).fit()
lmkw.f_pvalue
0.44688872149660885
Explanations#
Dummy coding options#
dmatrix("cat", data=catdf)
DesignMatrix with shape (4, 3)
Intercept cat[T.B] cat[T.C]
1 0 0
1 1 0
1 0 1
1 0 1
Terms:
'Intercept' (column 0)
'cat' (columns 1:3)
dmatrix("C(cat)", data=catdf)
DesignMatrix with shape (4, 3)
Intercept C(cat)[T.B] C(cat)[T.C]
1 0 0
1 1 0
1 0 1
1 0 1
Terms:
'Intercept' (column 0)
'C(cat)' (columns 1:3)
dmatrix("C(cat, Treatment)", data=catdf)
DesignMatrix with shape (4, 3)
Intercept C(cat, Treatment)[T.B] C(cat, Treatment)[T.C]
1 0 0
1 1 0
1 0 1
1 0 1
Terms:
'Intercept' (column 0)
'C(cat, Treatment)' (columns 1:3)
dmatrix("C(cat, Treatment('B'))", data=catdf)
# ALT. dmatrix("C(cat, Treatment(1))", data=catdf)
DesignMatrix with shape (4, 3)
Intercept C(cat, Treatment('B'))[T.A] C(cat, Treatment('B'))[T.C]
1 1 0
1 0 0
1 0 1
1 0 1
Terms:
'Intercept' (column 0)
"C(cat, Treatment('B'))" (columns 1:3)
Avoiding perfect collinearity#
df_col = pd.DataFrame()
df_col["iscli"] = (doctors["work"] == "cli").astype(int)
df_col["iseld"] = (doctors["work"] == "eld").astype(int)
df_col["ishos"] = (doctors["work"] == "hos").astype(int)
df_col["score"] = doctors["score"]
formula_col = "score ~ 1 + iscli + iseld + ishos"
lm_col = smf.ols(formula_col, data=df_col).fit()
lm_col.params
Intercept 36.718781
iscli 9.826673
iseld 14.396603
ishos 12.495504
dtype: float64
lm_col.condition_number
4594083276761821.0
lm2.params
Intercept 60.452901
alc -1.800101
weed -1.021552
exrc 1.768289
dtype: float64
Discussion#
Other coding strategies for categorical variables#
dmatrix("0 + C(cat)", data=catdf)
DesignMatrix with shape (4, 3)
C(cat)[A] C(cat)[B] C(cat)[C]
1 0 0
0 1 0
0 0 1
0 0 1
Terms:
'C(cat)' (columns 0:3)
dmatrix("1 + C(cat, Sum)", data=catdf)
DesignMatrix with shape (4, 3)
Intercept C(cat, Sum)[S.A] C(cat, Sum)[S.B]
1 1 0
1 0 1
1 -1 -1
1 -1 -1
Terms:
'Intercept' (column 0)
'C(cat, Sum)' (columns 1:3)
dmatrix("1+C(cat, Diff)", data=catdf)
DesignMatrix with shape (4, 3)
Intercept C(cat, Diff)[D.A] C(cat, Diff)[D.B]
1 -0.66667 -0.33333
1 0.33333 -0.33333
1 0.33333 0.66667
1 0.33333 0.66667
Terms:
'Intercept' (column 0)
'C(cat, Diff)' (columns 1:3)
dmatrix("C(cat, Helmert)", data=catdf)
DesignMatrix with shape (4, 3)
Intercept C(cat, Helmert)[H.B] C(cat, Helmert)[H.C]
1 -1 -1
1 1 -1
1 0 2
1 0 2
Terms:
'Intercept' (column 0)
'C(cat, Helmert)' (columns 1:3)
Exercises#
EXX: redo comparison of debate and lectures scores#
students = pd.read_csv("../datasets/students.csv")
lmcu = smf.ols("score ~ 1 + C(curriculum)", data=students).fit()
lmcu.tvalues.iloc[1], lmcu.pvalues.iloc[1]
(-1.7197867420465667, 0.10917234443214385)
EXX: model comparison#
formula3w = "score ~ 1 + alc + weed + exrc + C(loc) + C(work)"
lm3w = smf.ols(formula3w, data=doctors).fit()
formula3 = "score ~ 1 + alc + weed + exrc + C(loc)"
lm3 = smf.ols(formula3, data=doctors).fit()
lm3w.compare_f_test(lm3)
(1.5158185269522728, 0.22299549360240853, 2.0)
The result is non-significant which means including the predictor C(work)
in the model is not useful.
EXX: run ANOVA test#
# Construct data as a pd.DataFrame
np.random.seed(42)
As = np.random.normal(0, 1, 20)
Bs = np.random.normal(-2, 1, 20)
Cs = np.random.normal(3, 1, 20)
Ds = np.random.normal(1.5, 1, 20)
dfABCD = pd.DataFrame()
dfABCD["group"] = ["A"]*20 + ["B"]*20 + ["C"]*20 + ["D"]*20
dfABCD["value"] = np.concatenate([As, Bs, Cs, Ds])
with plt.rc_context({"figure.figsize":(8,6), "text.usetex":True}):
ax = plot_lm_anova(dfABCD, x="group", y="value")
from scipy.stats import f_oneway
resABCD = f_oneway(As, Bs, Cs, Ds)
print(resABCD.statistic, resABCD.pvalue)
lmabcd = smf.ols("value ~ C(group)", data=dfABCD).fit()
lmabcd.fvalue, lmabcd.f_pvalue
107.22963883851017 3.091116115443299e-27
(107.22963883851006, 3.091116115443401e-27)
Error in callback <function _draw_all_if_interactive at 0x7fdbe0cb3d90> (for post_execute), with arguments args (),kwargs {}:
---------------------------------------------------------------------------
FileNotFoundError Traceback (most recent call last)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/texmanager.py:247, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
246 try:
--> 247 report = subprocess.check_output(
248 command, cwd=cwd if cwd is not None else cls._texcache,
249 stderr=subprocess.STDOUT)
250 except FileNotFoundError as exc:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/subprocess.py:421, in check_output(timeout, *popenargs, **kwargs)
419 kwargs['input'] = empty
--> 421 return run(*popenargs, stdout=PIPE, timeout=timeout, check=True,
422 **kwargs).stdout
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/subprocess.py:503, in run(input, capture_output, timeout, check, *popenargs, **kwargs)
501 kwargs['stderr'] = PIPE
--> 503 with Popen(*popenargs, **kwargs) as process:
504 try:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/subprocess.py:971, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize)
968 self.stderr = io.TextIOWrapper(self.stderr,
969 encoding=encoding, errors=errors)
--> 971 self._execute_child(args, executable, preexec_fn, close_fds,
972 pass_fds, cwd, env,
973 startupinfo, creationflags, shell,
974 p2cread, p2cwrite,
975 c2pread, c2pwrite,
976 errread, errwrite,
977 restore_signals,
978 gid, gids, uid, umask,
979 start_new_session)
980 except:
981 # Cleanup if the child failed starting.
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/subprocess.py:1863, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session)
1862 err_msg = os.strerror(errno_num)
-> 1863 raise child_exception_type(errno_num, err_msg, err_filename)
1864 raise child_exception_type(err_msg)
FileNotFoundError: [Errno 2] No such file or directory: 'latex'
The above exception was the direct cause of the following exception:
RuntimeError Traceback (most recent call last)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/pyplot.py:279, in _draw_all_if_interactive()
277 def _draw_all_if_interactive() -> None:
278 if matplotlib.is_interactive():
--> 279 draw_all()
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/_pylab_helpers.py:131, in Gcf.draw_all(cls, force)
129 for manager in cls.get_all_fig_managers():
130 if force or manager.canvas.figure.stale:
--> 131 manager.canvas.draw_idle()
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/backend_bases.py:1891, in FigureCanvasBase.draw_idle(self, *args, **kwargs)
1889 if not self._is_idle_drawing:
1890 with self._idle_draw_cntx():
-> 1891 self.draw(*args, **kwargs)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/backends/backend_agg.py:382, in FigureCanvasAgg.draw(self)
379 # Acquire a lock on the shared font cache.
380 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
381 else nullcontext()):
--> 382 self.figure.draw(self.renderer)
383 # A GUI class may be need to update a window using this draw, so
384 # don't forget to call the superclass.
385 super().draw()
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/artist.py:94, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
92 @wraps(draw)
93 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 94 result = draw(artist, renderer, *args, **kwargs)
95 if renderer._rasterizing:
96 renderer.stop_rasterizing()
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/artist.py:71, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
68 if artist.get_agg_filter() is not None:
69 renderer.start_filter()
---> 71 return draw(artist, renderer)
72 finally:
73 if artist.get_agg_filter() is not None:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/figure.py:3257, in Figure.draw(self, renderer)
3254 # ValueError can occur when resizing a window.
3256 self.patch.draw(renderer)
-> 3257 mimage._draw_list_compositing_images(
3258 renderer, self, artists, self.suppressComposite)
3260 renderer.close_group('figure')
3261 finally:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/image.py:134, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
132 if not_composite or not has_images:
133 for a in artists:
--> 134 a.draw(renderer)
135 else:
136 # Composite any adjacent images together
137 image_group = []
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/artist.py:71, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
68 if artist.get_agg_filter() is not None:
69 renderer.start_filter()
---> 71 return draw(artist, renderer)
72 finally:
73 if artist.get_agg_filter() is not None:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/axes/_base.py:3181, in _AxesBase.draw(self, renderer)
3178 if artists_rasterized:
3179 _draw_rasterized(self.get_figure(root=True), artists_rasterized, renderer)
-> 3181 mimage._draw_list_compositing_images(
3182 renderer, self, artists, self.get_figure(root=True).suppressComposite)
3184 renderer.close_group('axes')
3185 self.stale = False
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/image.py:134, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
132 if not_composite or not has_images:
133 for a in artists:
--> 134 a.draw(renderer)
135 else:
136 # Composite any adjacent images together
137 image_group = []
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/artist.py:71, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
68 if artist.get_agg_filter() is not None:
69 renderer.start_filter()
---> 71 return draw(artist, renderer)
72 finally:
73 if artist.get_agg_filter() is not None:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/axis.py:1416, in Axis.draw(self, renderer)
1413 renderer.open_group(__name__, gid=self.get_gid())
1415 ticks_to_draw = self._update_ticks()
-> 1416 tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)
1418 for tick in ticks_to_draw:
1419 tick.draw(renderer)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/axis.py:1343, in Axis._get_ticklabel_bboxes(self, ticks, renderer)
1341 if renderer is None:
1342 renderer = self.get_figure(root=True)._get_renderer()
-> 1343 return ([tick.label1.get_window_extent(renderer)
1344 for tick in ticks if tick.label1.get_visible()],
1345 [tick.label2.get_window_extent(renderer)
1346 for tick in ticks if tick.label2.get_visible()])
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/axis.py:1343, in <listcomp>(.0)
1341 if renderer is None:
1342 renderer = self.get_figure(root=True)._get_renderer()
-> 1343 return ([tick.label1.get_window_extent(renderer)
1344 for tick in ticks if tick.label1.get_visible()],
1345 [tick.label2.get_window_extent(renderer)
1346 for tick in ticks if tick.label2.get_visible()])
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/text.py:969, in Text.get_window_extent(self, renderer, dpi)
964 raise RuntimeError(
965 "Cannot get window extent of text w/o renderer. You likely "
966 "want to call 'figure.draw_without_rendering()' first.")
968 with cbook._setattr_cm(fig, dpi=dpi):
--> 969 bbox, info, descent = self._get_layout(self._renderer)
970 x, y = self.get_unitless_position()
971 x, y = self.get_transform().transform((x, y))
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
370 ys = []
372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
374 renderer, "lp", self._fontproperties,
375 ismath="TeX" if self.get_usetex() else False,
376 dpi=self.get_figure(root=True).dpi)
377 min_dy = (lp_h - lp_d) * self._linespacing
379 for i, line in enumerate(lines):
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
67 # Cached based on a copy of fontprop so that later in-place mutations of
68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
70 weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
73 @functools.lru_cache(4096)
74 def _get_text_metrics_with_cache_impl(
75 renderer_ref, text, fontprop, ismath, dpi):
76 # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77 return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/backends/backend_agg.py:211, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
209 _api.check_in_list(["TeX", True, False], ismath=ismath)
210 if ismath == "TeX":
--> 211 return super().get_text_width_height_descent(s, prop, ismath)
213 if ismath:
214 ox, oy, width, height, descent, font_image = \
215 self.mathtext_parser.parse(s, self.dpi, prop)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/backend_bases.py:566, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
562 fontsize = prop.get_size_in_points()
564 if ismath == 'TeX':
565 # todo: handle properties
--> 566 return self.get_texmanager().get_text_width_height_descent(
567 s, fontsize, renderer=self)
569 dpi = self.points_to_pixels(72)
570 if ismath:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/texmanager.py:360, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
358 if tex.strip() == '':
359 return 0, 0, 0
--> 360 dvifile = cls.make_dvi(tex, fontsize)
361 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
362 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/texmanager.py:292, in TexManager.make_dvi(cls, tex, fontsize)
290 with TemporaryDirectory(dir=cwd) as tmpdir:
291 tmppath = Path(tmpdir)
--> 292 cls._run_checked_subprocess(
293 ["latex", "-interaction=nonstopmode", "--halt-on-error",
294 f"--output-directory={tmppath.name}",
295 f"{texfile.name}"], tex, cwd=cwd)
296 (tmppath / Path(dvifile).name).replace(dvifile)
297 return dvifile
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/texmanager.py:251, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
247 report = subprocess.check_output(
248 command, cwd=cwd if cwd is not None else cls._texcache,
249 stderr=subprocess.STDOUT)
250 except FileNotFoundError as exc:
--> 251 raise RuntimeError(
252 f'Failed to process string with tex because {command[0]} '
253 'could not be found') from exc
254 except subprocess.CalledProcessError as exc:
255 raise RuntimeError(
256 '{prog} was not able to process the following string:\n'
257 '{tex!r}\n\n'
(...)
264 exc=exc.output.decode('utf-8', 'backslashreplace'))
265 ) from None
RuntimeError: Failed to process string with tex because latex could not be found
---------------------------------------------------------------------------
FileNotFoundError Traceback (most recent call last)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/texmanager.py:247, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
246 try:
--> 247 report = subprocess.check_output(
248 command, cwd=cwd if cwd is not None else cls._texcache,
249 stderr=subprocess.STDOUT)
250 except FileNotFoundError as exc:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/subprocess.py:421, in check_output(timeout, *popenargs, **kwargs)
419 kwargs['input'] = empty
--> 421 return run(*popenargs, stdout=PIPE, timeout=timeout, check=True,
422 **kwargs).stdout
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/subprocess.py:503, in run(input, capture_output, timeout, check, *popenargs, **kwargs)
501 kwargs['stderr'] = PIPE
--> 503 with Popen(*popenargs, **kwargs) as process:
504 try:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/subprocess.py:971, in Popen.__init__(self, args, bufsize, executable, stdin, stdout, stderr, preexec_fn, close_fds, shell, cwd, env, universal_newlines, startupinfo, creationflags, restore_signals, start_new_session, pass_fds, user, group, extra_groups, encoding, errors, text, umask, pipesize)
968 self.stderr = io.TextIOWrapper(self.stderr,
969 encoding=encoding, errors=errors)
--> 971 self._execute_child(args, executable, preexec_fn, close_fds,
972 pass_fds, cwd, env,
973 startupinfo, creationflags, shell,
974 p2cread, p2cwrite,
975 c2pread, c2pwrite,
976 errread, errwrite,
977 restore_signals,
978 gid, gids, uid, umask,
979 start_new_session)
980 except:
981 # Cleanup if the child failed starting.
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/subprocess.py:1863, in Popen._execute_child(self, args, executable, preexec_fn, close_fds, pass_fds, cwd, env, startupinfo, creationflags, shell, p2cread, p2cwrite, c2pread, c2pwrite, errread, errwrite, restore_signals, gid, gids, uid, umask, start_new_session)
1862 err_msg = os.strerror(errno_num)
-> 1863 raise child_exception_type(errno_num, err_msg, err_filename)
1864 raise child_exception_type(err_msg)
FileNotFoundError: [Errno 2] No such file or directory: 'latex'
The above exception was the direct cause of the following exception:
RuntimeError Traceback (most recent call last)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/IPython/core/formatters.py:402, in BaseFormatter.__call__(self, obj)
400 pass
401 else:
--> 402 return printer(obj)
403 # Finally look for special method names
404 method = get_real_method(obj, self.print_method)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/IPython/core/pylabtools.py:187, in retina_figure(fig, base64, **kwargs)
178 def retina_figure(fig, base64=False, **kwargs):
179 """format a figure as a pixel-doubled (retina) PNG
180
181 If `base64` is True, return base64-encoded str instead of raw bytes
(...)
185 base64 argument
186 """
--> 187 pngdata = print_figure(fig, fmt="retina", base64=False, **kwargs)
188 # Make sure that retina_figure acts just like print_figure and returns
189 # None when the figure is empty.
190 if pngdata is None:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/IPython/core/pylabtools.py:170, in print_figure(fig, fmt, bbox_inches, base64, **kwargs)
167 from matplotlib.backend_bases import FigureCanvasBase
168 FigureCanvasBase(fig)
--> 170 fig.canvas.print_figure(bytes_io, **kw)
171 data = bytes_io.getvalue()
172 if fmt == 'svg':
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/backend_bases.py:2155, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
2152 # we do this instead of `self.figure.draw_without_rendering`
2153 # so that we can inject the orientation
2154 with getattr(renderer, "_draw_disabled", nullcontext)():
-> 2155 self.figure.draw(renderer)
2156 if bbox_inches:
2157 if bbox_inches == "tight":
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/artist.py:94, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
92 @wraps(draw)
93 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 94 result = draw(artist, renderer, *args, **kwargs)
95 if renderer._rasterizing:
96 renderer.stop_rasterizing()
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/artist.py:71, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
68 if artist.get_agg_filter() is not None:
69 renderer.start_filter()
---> 71 return draw(artist, renderer)
72 finally:
73 if artist.get_agg_filter() is not None:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/figure.py:3257, in Figure.draw(self, renderer)
3254 # ValueError can occur when resizing a window.
3256 self.patch.draw(renderer)
-> 3257 mimage._draw_list_compositing_images(
3258 renderer, self, artists, self.suppressComposite)
3260 renderer.close_group('figure')
3261 finally:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/image.py:134, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
132 if not_composite or not has_images:
133 for a in artists:
--> 134 a.draw(renderer)
135 else:
136 # Composite any adjacent images together
137 image_group = []
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/artist.py:71, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
68 if artist.get_agg_filter() is not None:
69 renderer.start_filter()
---> 71 return draw(artist, renderer)
72 finally:
73 if artist.get_agg_filter() is not None:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/axes/_base.py:3181, in _AxesBase.draw(self, renderer)
3178 if artists_rasterized:
3179 _draw_rasterized(self.get_figure(root=True), artists_rasterized, renderer)
-> 3181 mimage._draw_list_compositing_images(
3182 renderer, self, artists, self.get_figure(root=True).suppressComposite)
3184 renderer.close_group('axes')
3185 self.stale = False
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/image.py:134, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
132 if not_composite or not has_images:
133 for a in artists:
--> 134 a.draw(renderer)
135 else:
136 # Composite any adjacent images together
137 image_group = []
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/artist.py:71, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
68 if artist.get_agg_filter() is not None:
69 renderer.start_filter()
---> 71 return draw(artist, renderer)
72 finally:
73 if artist.get_agg_filter() is not None:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/axis.py:1416, in Axis.draw(self, renderer)
1413 renderer.open_group(__name__, gid=self.get_gid())
1415 ticks_to_draw = self._update_ticks()
-> 1416 tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)
1418 for tick in ticks_to_draw:
1419 tick.draw(renderer)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/axis.py:1343, in Axis._get_ticklabel_bboxes(self, ticks, renderer)
1341 if renderer is None:
1342 renderer = self.get_figure(root=True)._get_renderer()
-> 1343 return ([tick.label1.get_window_extent(renderer)
1344 for tick in ticks if tick.label1.get_visible()],
1345 [tick.label2.get_window_extent(renderer)
1346 for tick in ticks if tick.label2.get_visible()])
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/axis.py:1343, in <listcomp>(.0)
1341 if renderer is None:
1342 renderer = self.get_figure(root=True)._get_renderer()
-> 1343 return ([tick.label1.get_window_extent(renderer)
1344 for tick in ticks if tick.label1.get_visible()],
1345 [tick.label2.get_window_extent(renderer)
1346 for tick in ticks if tick.label2.get_visible()])
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/text.py:969, in Text.get_window_extent(self, renderer, dpi)
964 raise RuntimeError(
965 "Cannot get window extent of text w/o renderer. You likely "
966 "want to call 'figure.draw_without_rendering()' first.")
968 with cbook._setattr_cm(fig, dpi=dpi):
--> 969 bbox, info, descent = self._get_layout(self._renderer)
970 x, y = self.get_unitless_position()
971 x, y = self.get_transform().transform((x, y))
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/text.py:373, in Text._get_layout(self, renderer)
370 ys = []
372 # Full vertical extent of font, including ascenders and descenders:
--> 373 _, lp_h, lp_d = _get_text_metrics_with_cache(
374 renderer, "lp", self._fontproperties,
375 ismath="TeX" if self.get_usetex() else False,
376 dpi=self.get_figure(root=True).dpi)
377 min_dy = (lp_h - lp_d) * self._linespacing
379 for i, line in enumerate(lines):
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/text.py:69, in _get_text_metrics_with_cache(renderer, text, fontprop, ismath, dpi)
66 """Call ``renderer.get_text_width_height_descent``, caching the results."""
67 # Cached based on a copy of fontprop so that later in-place mutations of
68 # the passed-in argument do not mess up the cache.
---> 69 return _get_text_metrics_with_cache_impl(
70 weakref.ref(renderer), text, fontprop.copy(), ismath, dpi)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/text.py:77, in _get_text_metrics_with_cache_impl(renderer_ref, text, fontprop, ismath, dpi)
73 @functools.lru_cache(4096)
74 def _get_text_metrics_with_cache_impl(
75 renderer_ref, text, fontprop, ismath, dpi):
76 # dpi is unused, but participates in cache invalidation (via the renderer).
---> 77 return renderer_ref().get_text_width_height_descent(text, fontprop, ismath)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/backends/backend_agg.py:211, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
209 _api.check_in_list(["TeX", True, False], ismath=ismath)
210 if ismath == "TeX":
--> 211 return super().get_text_width_height_descent(s, prop, ismath)
213 if ismath:
214 ox, oy, width, height, descent, font_image = \
215 self.mathtext_parser.parse(s, self.dpi, prop)
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/backend_bases.py:566, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
562 fontsize = prop.get_size_in_points()
564 if ismath == 'TeX':
565 # todo: handle properties
--> 566 return self.get_texmanager().get_text_width_height_descent(
567 s, fontsize, renderer=self)
569 dpi = self.points_to_pixels(72)
570 if ismath:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/texmanager.py:360, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
358 if tex.strip() == '':
359 return 0, 0, 0
--> 360 dvifile = cls.make_dvi(tex, fontsize)
361 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
362 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/texmanager.py:292, in TexManager.make_dvi(cls, tex, fontsize)
290 with TemporaryDirectory(dir=cwd) as tmpdir:
291 tmppath = Path(tmpdir)
--> 292 cls._run_checked_subprocess(
293 ["latex", "-interaction=nonstopmode", "--halt-on-error",
294 f"--output-directory={tmppath.name}",
295 f"{texfile.name}"], tex, cwd=cwd)
296 (tmppath / Path(dvifile).name).replace(dvifile)
297 return dvifile
File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/matplotlib/texmanager.py:251, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
247 report = subprocess.check_output(
248 command, cwd=cwd if cwd is not None else cls._texcache,
249 stderr=subprocess.STDOUT)
250 except FileNotFoundError as exc:
--> 251 raise RuntimeError(
252 f'Failed to process string with tex because {command[0]} '
253 'could not be found') from exc
254 except subprocess.CalledProcessError as exc:
255 raise RuntimeError(
256 '{prog} was not able to process the following string:\n'
257 '{tex!r}\n\n'
(...)
264 exc=exc.output.decode('utf-8', 'backslashreplace'))
265 ) from None
RuntimeError: Failed to process string with tex because latex could not be found
<Figure size 800x600 with 1 Axes>
Links#
Patsy and Statsmodels https://www.youtube.com/watch?v=iEANEcWqAx4
Tests as LMs: https://lindeloev.github.io/tests-as-linear/
https://danielroelfs.com/blog/everything-is-a-linear-model/ via HN