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

Visualization of the results of the model .

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

Visualization of the estimated parameters of the model .

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");
../_images/baa9f4d5d9f7b7c6b20f8e835dad22ef51523e45b35a0d2cd620c6a10df87db8.png
lm3.summary()
OLS Regression Results
Dep. Variable: score R-squared: 0.854
Model: OLS Adj. R-squared: 0.851
Method: Least Squares F-statistic: 221.6
Date: Fri, 18 Oct 2024 Prob (F-statistic): 4.18e-62
Time: 20:56:14 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, 0.003705665350332633)

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])

Visualization of the comparison between the two groups.

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 0x7efc24f5e280> (for post_execute), with arguments args (),kwargs {}:
---------------------------------------------------------------------------
FileNotFoundError                         Traceback (most recent call last)
File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/texmanager.py:250, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
    249 try:
--> 250     report = subprocess.check_output(
    251         command, cwd=cwd if cwd is not None else cls._texcache,
    252         stderr=subprocess.STDOUT)
    253 except FileNotFoundError as exc:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/subprocess.py:424, in check_output(timeout, *popenargs, **kwargs)
    422     kwargs['input'] = empty
--> 424 return run(*popenargs, stdout=PIPE, timeout=timeout, check=True,
    425            **kwargs).stdout

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/subprocess.py:505, in run(input, capture_output, timeout, check, *popenargs, **kwargs)
    503     kwargs['stderr'] = PIPE
--> 505 with Popen(*popenargs, **kwargs) as process:
    506     try:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/subprocess.py:951, 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)
    948             self.stderr = io.TextIOWrapper(self.stderr,
    949                     encoding=encoding, errors=errors)
--> 951     self._execute_child(args, executable, preexec_fn, close_fds,
    952                         pass_fds, cwd, env,
    953                         startupinfo, creationflags, shell,
    954                         p2cread, p2cwrite,
    955                         c2pread, c2pwrite,
    956                         errread, errwrite,
    957                         restore_signals,
    958                         gid, gids, uid, umask,
    959                         start_new_session)
    960 except:
    961     # Cleanup if the child failed starting.

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/subprocess.py:1837, 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)
   1836         err_msg = os.strerror(errno_num)
-> 1837     raise child_exception_type(errno_num, err_msg, err_filename)
   1838 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/3.9.20/x64/lib/python3.9/site-packages/matplotlib/pyplot.py:268, in _draw_all_if_interactive()
    266 def _draw_all_if_interactive() -> None:
    267     if matplotlib.is_interactive():
--> 268         draw_all()

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/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/3.9.20/x64/lib/python3.9/site-packages/matplotlib/backend_bases.py:1905, in FigureCanvasBase.draw_idle(self, *args, **kwargs)
   1903 if not self._is_idle_drawing:
   1904     with self._idle_draw_cntx():
-> 1905         self.draw(*args, **kwargs)

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/backends/backend_agg.py:387, in FigureCanvasAgg.draw(self)
    384 # Acquire a lock on the shared font cache.
    385 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    386       else nullcontext()):
--> 387     self.figure.draw(self.renderer)
    388     # A GUI class may be need to update a window using this draw, so
    389     # don't forget to call the superclass.
    390     super().draw()

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/figure.py:3162, in Figure.draw(self, renderer)
   3159             # ValueError can occur when resizing a window.
   3161     self.patch.draw(renderer)
-> 3162     mimage._draw_list_compositing_images(
   3163         renderer, self, artists, self.suppressComposite)
   3165     renderer.close_group('figure')
   3166 finally:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axes/_base.py:3101, in _AxesBase.draw(self, renderer)
   3098     for spine in self.spines.values():
   3099         artists.remove(spine)
-> 3101 self._update_title_position(renderer)
   3103 if not self.axison:
   3104     for _axis in self._axis_map.values():

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axes/_base.py:3036, in _AxesBase._update_title_position(self, renderer)
   3033 bb = None
   3034 if (ax.xaxis.get_ticks_position() in ['top', 'unknown']
   3035         or ax.xaxis.get_label_position() == 'top'):
-> 3036     bb = ax.xaxis.get_tightbbox(renderer)
   3037 if bb is None:
   3038     if 'outline' in ax.spines:
   3039         # Special case for colorbars:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axis.py:1372, in Axis.get_tightbbox(self, renderer, for_layout_only)
   1369     renderer = self.figure._get_renderer()
   1370 ticks_to_draw = self._update_ticks()
-> 1372 self._update_label_position(renderer)
   1374 # go back to just this axis's tick labels
   1375 tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axis.py:2413, in XAxis._update_label_position(self, renderer)
   2409     return
   2411 # get bounding boxes for this axis and any siblings
   2412 # that have been set by `fig.align_xlabels()`
-> 2413 bboxes, bboxes2 = self._get_tick_boxes_siblings(renderer=renderer)
   2415 x, y = self.label.get_position()
   2416 if self.label_position == 'bottom':

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axis.py:2206, in Axis._get_tick_boxes_siblings(self, renderer)
   2204 axis = ax._axis_map[name]
   2205 ticks_to_draw = axis._update_ticks()
-> 2206 tlb, tlb2 = axis._get_ticklabel_bboxes(ticks_to_draw, renderer)
   2207 bboxes.extend(tlb)
   2208 bboxes2.extend(tlb2)

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axis.py:1351, in Axis._get_ticklabel_bboxes(self, ticks, renderer)
   1349 if renderer is None:
   1350     renderer = self.figure._get_renderer()
-> 1351 return ([tick.label1.get_window_extent(renderer)
   1352          for tick in ticks if tick.label1.get_visible()],
   1353         [tick.label2.get_window_extent(renderer)
   1354          for tick in ticks if tick.label2.get_visible()])

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axis.py:1351, in <listcomp>(.0)
   1349 if renderer is None:
   1350     renderer = self.figure._get_renderer()
-> 1351 return ([tick.label1.get_window_extent(renderer)
   1352          for tick in ticks if tick.label1.get_visible()],
   1353         [tick.label2.get_window_extent(renderer)
   1354          for tick in ticks if tick.label2.get_visible()])

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/text.py:959, in Text.get_window_extent(self, renderer, dpi)
    954     raise RuntimeError(
    955         "Cannot get window extent of text w/o renderer. You likely "
    956         "want to call 'figure.draw_without_rendering()' first.")
    958 with cbook._setattr_cm(self.figure, dpi=dpi):
--> 959     bbox, info, descent = self._get_layout(self._renderer)
    960     x, y = self.get_unitless_position()
    961     x, y = self.get_transform().transform((x, y))

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/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, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/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/3.9.20/x64/lib/python3.9/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/3.9.20/x64/lib/python3.9/site-packages/matplotlib/backends/backend_agg.py:212, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    210 _api.check_in_list(["TeX", True, False], ismath=ismath)
    211 if ismath == "TeX":
--> 212     return super().get_text_width_height_descent(s, prop, ismath)
    214 if ismath:
    215     ox, oy, width, height, descent, font_image = \
    216         self.mathtext_parser.parse(s, self.dpi, prop)

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/backend_bases.py:597, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    593 fontsize = prop.get_size_in_points()
    595 if ismath == 'TeX':
    596     # todo: handle properties
--> 597     return self.get_texmanager().get_text_width_height_descent(
    598         s, fontsize, renderer=self)
    600 dpi = self.points_to_pixels(72)
    601 if ismath:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/texmanager.py:363, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    361 if tex.strip() == '':
    362     return 0, 0, 0
--> 363 dvifile = cls.make_dvi(tex, fontsize)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/texmanager.py:295, in TexManager.make_dvi(cls, tex, fontsize)
    293     with TemporaryDirectory(dir=cwd) as tmpdir:
    294         tmppath = Path(tmpdir)
--> 295         cls._run_checked_subprocess(
    296             ["latex", "-interaction=nonstopmode", "--halt-on-error",
    297              f"--output-directory={tmppath.name}",
    298              f"{texfile.name}"], tex, cwd=cwd)
    299         (tmppath / Path(dvifile).name).replace(dvifile)
    300 return dvifile

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/texmanager.py:254, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
    250     report = subprocess.check_output(
    251         command, cwd=cwd if cwd is not None else cls._texcache,
    252         stderr=subprocess.STDOUT)
    253 except FileNotFoundError as exc:
--> 254     raise RuntimeError(
    255         f'Failed to process string with tex because {command[0]} '
    256         'could not be found') from exc
    257 except subprocess.CalledProcessError as exc:
    258     raise RuntimeError(
    259         '{prog} was not able to process the following string:\n'
    260         '{tex!r}\n\n'
   (...)
    267             exc=exc.output.decode('utf-8', 'backslashreplace'))
    268         ) 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/3.9.20/x64/lib/python3.9/site-packages/matplotlib/texmanager.py:250, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
    249 try:
--> 250     report = subprocess.check_output(
    251         command, cwd=cwd if cwd is not None else cls._texcache,
    252         stderr=subprocess.STDOUT)
    253 except FileNotFoundError as exc:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/subprocess.py:424, in check_output(timeout, *popenargs, **kwargs)
    422     kwargs['input'] = empty
--> 424 return run(*popenargs, stdout=PIPE, timeout=timeout, check=True,
    425            **kwargs).stdout

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/subprocess.py:505, in run(input, capture_output, timeout, check, *popenargs, **kwargs)
    503     kwargs['stderr'] = PIPE
--> 505 with Popen(*popenargs, **kwargs) as process:
    506     try:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/subprocess.py:951, 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)
    948             self.stderr = io.TextIOWrapper(self.stderr,
    949                     encoding=encoding, errors=errors)
--> 951     self._execute_child(args, executable, preexec_fn, close_fds,
    952                         pass_fds, cwd, env,
    953                         startupinfo, creationflags, shell,
    954                         p2cread, p2cwrite,
    955                         c2pread, c2pwrite,
    956                         errread, errwrite,
    957                         restore_signals,
    958                         gid, gids, uid, umask,
    959                         start_new_session)
    960 except:
    961     # Cleanup if the child failed starting.

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/subprocess.py:1837, 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)
   1836         err_msg = os.strerror(errno_num)
-> 1837     raise child_exception_type(errno_num, err_msg, err_filename)
   1838 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/3.9.20/x64/lib/python3.9/site-packages/IPython/core/formatters.py:340, in BaseFormatter.__call__(self, obj)
    338     pass
    339 else:
--> 340     return printer(obj)
    341 # Finally look for special method names
    342 method = get_real_method(obj, self.print_method)

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/IPython/core/pylabtools.py:169, in retina_figure(fig, base64, **kwargs)
    160 def retina_figure(fig, base64=False, **kwargs):
    161     """format a figure as a pixel-doubled (retina) PNG
    162 
    163     If `base64` is True, return base64-encoded str instead of raw bytes
   (...)
    167         base64 argument
    168     """
--> 169     pngdata = print_figure(fig, fmt="retina", base64=False, **kwargs)
    170     # Make sure that retina_figure acts just like print_figure and returns
    171     # None when the figure is empty.
    172     if pngdata is None:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/IPython/core/pylabtools.py:152, in print_figure(fig, fmt, bbox_inches, base64, **kwargs)
    149     from matplotlib.backend_bases import FigureCanvasBase
    150     FigureCanvasBase(fig)
--> 152 fig.canvas.print_figure(bytes_io, **kw)
    153 data = bytes_io.getvalue()
    154 if fmt == 'svg':

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/backend_bases.py:2175, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2172     # we do this instead of `self.figure.draw_without_rendering`
   2173     # so that we can inject the orientation
   2174     with getattr(renderer, "_draw_disabled", nullcontext)():
-> 2175         self.figure.draw(renderer)
   2176 if bbox_inches:
   2177     if bbox_inches == "tight":

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/figure.py:3162, in Figure.draw(self, renderer)
   3159             # ValueError can occur when resizing a window.
   3161     self.patch.draw(renderer)
-> 3162     mimage._draw_list_compositing_images(
   3163         renderer, self, artists, self.suppressComposite)
   3165     renderer.close_group('figure')
   3166 finally:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axes/_base.py:3101, in _AxesBase.draw(self, renderer)
   3098     for spine in self.spines.values():
   3099         artists.remove(spine)
-> 3101 self._update_title_position(renderer)
   3103 if not self.axison:
   3104     for _axis in self._axis_map.values():

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axes/_base.py:3036, in _AxesBase._update_title_position(self, renderer)
   3033 bb = None
   3034 if (ax.xaxis.get_ticks_position() in ['top', 'unknown']
   3035         or ax.xaxis.get_label_position() == 'top'):
-> 3036     bb = ax.xaxis.get_tightbbox(renderer)
   3037 if bb is None:
   3038     if 'outline' in ax.spines:
   3039         # Special case for colorbars:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axis.py:1372, in Axis.get_tightbbox(self, renderer, for_layout_only)
   1369     renderer = self.figure._get_renderer()
   1370 ticks_to_draw = self._update_ticks()
-> 1372 self._update_label_position(renderer)
   1374 # go back to just this axis's tick labels
   1375 tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axis.py:2413, in XAxis._update_label_position(self, renderer)
   2409     return
   2411 # get bounding boxes for this axis and any siblings
   2412 # that have been set by `fig.align_xlabels()`
-> 2413 bboxes, bboxes2 = self._get_tick_boxes_siblings(renderer=renderer)
   2415 x, y = self.label.get_position()
   2416 if self.label_position == 'bottom':

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axis.py:2206, in Axis._get_tick_boxes_siblings(self, renderer)
   2204 axis = ax._axis_map[name]
   2205 ticks_to_draw = axis._update_ticks()
-> 2206 tlb, tlb2 = axis._get_ticklabel_bboxes(ticks_to_draw, renderer)
   2207 bboxes.extend(tlb)
   2208 bboxes2.extend(tlb2)

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axis.py:1351, in Axis._get_ticklabel_bboxes(self, ticks, renderer)
   1349 if renderer is None:
   1350     renderer = self.figure._get_renderer()
-> 1351 return ([tick.label1.get_window_extent(renderer)
   1352          for tick in ticks if tick.label1.get_visible()],
   1353         [tick.label2.get_window_extent(renderer)
   1354          for tick in ticks if tick.label2.get_visible()])

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axis.py:1351, in <listcomp>(.0)
   1349 if renderer is None:
   1350     renderer = self.figure._get_renderer()
-> 1351 return ([tick.label1.get_window_extent(renderer)
   1352          for tick in ticks if tick.label1.get_visible()],
   1353         [tick.label2.get_window_extent(renderer)
   1354          for tick in ticks if tick.label2.get_visible()])

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/text.py:959, in Text.get_window_extent(self, renderer, dpi)
    954     raise RuntimeError(
    955         "Cannot get window extent of text w/o renderer. You likely "
    956         "want to call 'figure.draw_without_rendering()' first.")
    958 with cbook._setattr_cm(self.figure, dpi=dpi):
--> 959     bbox, info, descent = self._get_layout(self._renderer)
    960     x, y = self.get_unitless_position()
    961     x, y = self.get_transform().transform((x, y))

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/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, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/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/3.9.20/x64/lib/python3.9/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/3.9.20/x64/lib/python3.9/site-packages/matplotlib/backends/backend_agg.py:212, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    210 _api.check_in_list(["TeX", True, False], ismath=ismath)
    211 if ismath == "TeX":
--> 212     return super().get_text_width_height_descent(s, prop, ismath)
    214 if ismath:
    215     ox, oy, width, height, descent, font_image = \
    216         self.mathtext_parser.parse(s, self.dpi, prop)

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/backend_bases.py:597, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    593 fontsize = prop.get_size_in_points()
    595 if ismath == 'TeX':
    596     # todo: handle properties
--> 597     return self.get_texmanager().get_text_width_height_descent(
    598         s, fontsize, renderer=self)
    600 dpi = self.points_to_pixels(72)
    601 if ismath:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/texmanager.py:363, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    361 if tex.strip() == '':
    362     return 0, 0, 0
--> 363 dvifile = cls.make_dvi(tex, fontsize)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/texmanager.py:295, in TexManager.make_dvi(cls, tex, fontsize)
    293     with TemporaryDirectory(dir=cwd) as tmpdir:
    294         tmppath = Path(tmpdir)
--> 295         cls._run_checked_subprocess(
    296             ["latex", "-interaction=nonstopmode", "--halt-on-error",
    297              f"--output-directory={tmppath.name}",
    298              f"{texfile.name}"], tex, cwd=cwd)
    299         (tmppath / Path(dvifile).name).replace(dvifile)
    300 return dvifile

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/texmanager.py:254, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
    250     report = subprocess.check_output(
    251         command, cwd=cwd if cwd is not None else cls._texcache,
    252         stderr=subprocess.STDOUT)
    253 except FileNotFoundError as exc:
--> 254     raise RuntimeError(
    255         f'Failed to process string with tex because {command[0]} '
    256         'could not be found') from exc
    257 except subprocess.CalledProcessError as exc:
    258     raise RuntimeError(
    259         '{prog} was not able to process the following string:\n'
    260         '{tex!r}\n\n'
   (...)
    267             exc=exc.output.decode('utf-8', 'backslashreplace'))
    268         ) 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 0x7efc24f5e280> (for post_execute), with arguments args (),kwargs {}:
---------------------------------------------------------------------------
FileNotFoundError                         Traceback (most recent call last)
File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/texmanager.py:250, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
    249 try:
--> 250     report = subprocess.check_output(
    251         command, cwd=cwd if cwd is not None else cls._texcache,
    252         stderr=subprocess.STDOUT)
    253 except FileNotFoundError as exc:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/subprocess.py:424, in check_output(timeout, *popenargs, **kwargs)
    422     kwargs['input'] = empty
--> 424 return run(*popenargs, stdout=PIPE, timeout=timeout, check=True,
    425            **kwargs).stdout

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/subprocess.py:505, in run(input, capture_output, timeout, check, *popenargs, **kwargs)
    503     kwargs['stderr'] = PIPE
--> 505 with Popen(*popenargs, **kwargs) as process:
    506     try:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/subprocess.py:951, 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)
    948             self.stderr = io.TextIOWrapper(self.stderr,
    949                     encoding=encoding, errors=errors)
--> 951     self._execute_child(args, executable, preexec_fn, close_fds,
    952                         pass_fds, cwd, env,
    953                         startupinfo, creationflags, shell,
    954                         p2cread, p2cwrite,
    955                         c2pread, c2pwrite,
    956                         errread, errwrite,
    957                         restore_signals,
    958                         gid, gids, uid, umask,
    959                         start_new_session)
    960 except:
    961     # Cleanup if the child failed starting.

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/subprocess.py:1837, 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)
   1836         err_msg = os.strerror(errno_num)
-> 1837     raise child_exception_type(errno_num, err_msg, err_filename)
   1838 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/3.9.20/x64/lib/python3.9/site-packages/matplotlib/pyplot.py:268, in _draw_all_if_interactive()
    266 def _draw_all_if_interactive() -> None:
    267     if matplotlib.is_interactive():
--> 268         draw_all()

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/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/3.9.20/x64/lib/python3.9/site-packages/matplotlib/backend_bases.py:1905, in FigureCanvasBase.draw_idle(self, *args, **kwargs)
   1903 if not self._is_idle_drawing:
   1904     with self._idle_draw_cntx():
-> 1905         self.draw(*args, **kwargs)

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/backends/backend_agg.py:387, in FigureCanvasAgg.draw(self)
    384 # Acquire a lock on the shared font cache.
    385 with (self.toolbar._wait_cursor_for_draw_cm() if self.toolbar
    386       else nullcontext()):
--> 387     self.figure.draw(self.renderer)
    388     # A GUI class may be need to update a window using this draw, so
    389     # don't forget to call the superclass.
    390     super().draw()

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/figure.py:3162, in Figure.draw(self, renderer)
   3159             # ValueError can occur when resizing a window.
   3161     self.patch.draw(renderer)
-> 3162     mimage._draw_list_compositing_images(
   3163         renderer, self, artists, self.suppressComposite)
   3165     renderer.close_group('figure')
   3166 finally:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axes/_base.py:3101, in _AxesBase.draw(self, renderer)
   3098     for spine in self.spines.values():
   3099         artists.remove(spine)
-> 3101 self._update_title_position(renderer)
   3103 if not self.axison:
   3104     for _axis in self._axis_map.values():

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axes/_base.py:3036, in _AxesBase._update_title_position(self, renderer)
   3033 bb = None
   3034 if (ax.xaxis.get_ticks_position() in ['top', 'unknown']
   3035         or ax.xaxis.get_label_position() == 'top'):
-> 3036     bb = ax.xaxis.get_tightbbox(renderer)
   3037 if bb is None:
   3038     if 'outline' in ax.spines:
   3039         # Special case for colorbars:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axis.py:1372, in Axis.get_tightbbox(self, renderer, for_layout_only)
   1369     renderer = self.figure._get_renderer()
   1370 ticks_to_draw = self._update_ticks()
-> 1372 self._update_label_position(renderer)
   1374 # go back to just this axis's tick labels
   1375 tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axis.py:2413, in XAxis._update_label_position(self, renderer)
   2409     return
   2411 # get bounding boxes for this axis and any siblings
   2412 # that have been set by `fig.align_xlabels()`
-> 2413 bboxes, bboxes2 = self._get_tick_boxes_siblings(renderer=renderer)
   2415 x, y = self.label.get_position()
   2416 if self.label_position == 'bottom':

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axis.py:2206, in Axis._get_tick_boxes_siblings(self, renderer)
   2204 axis = ax._axis_map[name]
   2205 ticks_to_draw = axis._update_ticks()
-> 2206 tlb, tlb2 = axis._get_ticklabel_bboxes(ticks_to_draw, renderer)
   2207 bboxes.extend(tlb)
   2208 bboxes2.extend(tlb2)

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axis.py:1351, in Axis._get_ticklabel_bboxes(self, ticks, renderer)
   1349 if renderer is None:
   1350     renderer = self.figure._get_renderer()
-> 1351 return ([tick.label1.get_window_extent(renderer)
   1352          for tick in ticks if tick.label1.get_visible()],
   1353         [tick.label2.get_window_extent(renderer)
   1354          for tick in ticks if tick.label2.get_visible()])

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axis.py:1351, in <listcomp>(.0)
   1349 if renderer is None:
   1350     renderer = self.figure._get_renderer()
-> 1351 return ([tick.label1.get_window_extent(renderer)
   1352          for tick in ticks if tick.label1.get_visible()],
   1353         [tick.label2.get_window_extent(renderer)
   1354          for tick in ticks if tick.label2.get_visible()])

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/text.py:959, in Text.get_window_extent(self, renderer, dpi)
    954     raise RuntimeError(
    955         "Cannot get window extent of text w/o renderer. You likely "
    956         "want to call 'figure.draw_without_rendering()' first.")
    958 with cbook._setattr_cm(self.figure, dpi=dpi):
--> 959     bbox, info, descent = self._get_layout(self._renderer)
    960     x, y = self.get_unitless_position()
    961     x, y = self.get_transform().transform((x, y))

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/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, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/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/3.9.20/x64/lib/python3.9/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/3.9.20/x64/lib/python3.9/site-packages/matplotlib/backends/backend_agg.py:212, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    210 _api.check_in_list(["TeX", True, False], ismath=ismath)
    211 if ismath == "TeX":
--> 212     return super().get_text_width_height_descent(s, prop, ismath)
    214 if ismath:
    215     ox, oy, width, height, descent, font_image = \
    216         self.mathtext_parser.parse(s, self.dpi, prop)

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/backend_bases.py:597, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    593 fontsize = prop.get_size_in_points()
    595 if ismath == 'TeX':
    596     # todo: handle properties
--> 597     return self.get_texmanager().get_text_width_height_descent(
    598         s, fontsize, renderer=self)
    600 dpi = self.points_to_pixels(72)
    601 if ismath:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/texmanager.py:363, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    361 if tex.strip() == '':
    362     return 0, 0, 0
--> 363 dvifile = cls.make_dvi(tex, fontsize)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/texmanager.py:295, in TexManager.make_dvi(cls, tex, fontsize)
    293     with TemporaryDirectory(dir=cwd) as tmpdir:
    294         tmppath = Path(tmpdir)
--> 295         cls._run_checked_subprocess(
    296             ["latex", "-interaction=nonstopmode", "--halt-on-error",
    297              f"--output-directory={tmppath.name}",
    298              f"{texfile.name}"], tex, cwd=cwd)
    299         (tmppath / Path(dvifile).name).replace(dvifile)
    300 return dvifile

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/texmanager.py:254, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
    250     report = subprocess.check_output(
    251         command, cwd=cwd if cwd is not None else cls._texcache,
    252         stderr=subprocess.STDOUT)
    253 except FileNotFoundError as exc:
--> 254     raise RuntimeError(
    255         f'Failed to process string with tex because {command[0]} '
    256         'could not be found') from exc
    257 except subprocess.CalledProcessError as exc:
    258     raise RuntimeError(
    259         '{prog} was not able to process the following string:\n'
    260         '{tex!r}\n\n'
   (...)
    267             exc=exc.output.decode('utf-8', 'backslashreplace'))
    268         ) 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/3.9.20/x64/lib/python3.9/site-packages/matplotlib/texmanager.py:250, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
    249 try:
--> 250     report = subprocess.check_output(
    251         command, cwd=cwd if cwd is not None else cls._texcache,
    252         stderr=subprocess.STDOUT)
    253 except FileNotFoundError as exc:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/subprocess.py:424, in check_output(timeout, *popenargs, **kwargs)
    422     kwargs['input'] = empty
--> 424 return run(*popenargs, stdout=PIPE, timeout=timeout, check=True,
    425            **kwargs).stdout

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/subprocess.py:505, in run(input, capture_output, timeout, check, *popenargs, **kwargs)
    503     kwargs['stderr'] = PIPE
--> 505 with Popen(*popenargs, **kwargs) as process:
    506     try:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/subprocess.py:951, 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)
    948             self.stderr = io.TextIOWrapper(self.stderr,
    949                     encoding=encoding, errors=errors)
--> 951     self._execute_child(args, executable, preexec_fn, close_fds,
    952                         pass_fds, cwd, env,
    953                         startupinfo, creationflags, shell,
    954                         p2cread, p2cwrite,
    955                         c2pread, c2pwrite,
    956                         errread, errwrite,
    957                         restore_signals,
    958                         gid, gids, uid, umask,
    959                         start_new_session)
    960 except:
    961     # Cleanup if the child failed starting.

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/subprocess.py:1837, 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)
   1836         err_msg = os.strerror(errno_num)
-> 1837     raise child_exception_type(errno_num, err_msg, err_filename)
   1838 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/3.9.20/x64/lib/python3.9/site-packages/IPython/core/formatters.py:340, in BaseFormatter.__call__(self, obj)
    338     pass
    339 else:
--> 340     return printer(obj)
    341 # Finally look for special method names
    342 method = get_real_method(obj, self.print_method)

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/IPython/core/pylabtools.py:169, in retina_figure(fig, base64, **kwargs)
    160 def retina_figure(fig, base64=False, **kwargs):
    161     """format a figure as a pixel-doubled (retina) PNG
    162 
    163     If `base64` is True, return base64-encoded str instead of raw bytes
   (...)
    167         base64 argument
    168     """
--> 169     pngdata = print_figure(fig, fmt="retina", base64=False, **kwargs)
    170     # Make sure that retina_figure acts just like print_figure and returns
    171     # None when the figure is empty.
    172     if pngdata is None:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/IPython/core/pylabtools.py:152, in print_figure(fig, fmt, bbox_inches, base64, **kwargs)
    149     from matplotlib.backend_bases import FigureCanvasBase
    150     FigureCanvasBase(fig)
--> 152 fig.canvas.print_figure(bytes_io, **kw)
    153 data = bytes_io.getvalue()
    154 if fmt == 'svg':

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/backend_bases.py:2175, in FigureCanvasBase.print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)
   2172     # we do this instead of `self.figure.draw_without_rendering`
   2173     # so that we can inject the orientation
   2174     with getattr(renderer, "_draw_disabled", nullcontext)():
-> 2175         self.figure.draw(renderer)
   2176 if bbox_inches:
   2177     if bbox_inches == "tight":

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/artist.py:95, in _finalize_rasterization.<locals>.draw_wrapper(artist, renderer, *args, **kwargs)
     93 @wraps(draw)
     94 def draw_wrapper(artist, renderer, *args, **kwargs):
---> 95     result = draw(artist, renderer, *args, **kwargs)
     96     if renderer._rasterizing:
     97         renderer.stop_rasterizing()

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/figure.py:3162, in Figure.draw(self, renderer)
   3159             # ValueError can occur when resizing a window.
   3161     self.patch.draw(renderer)
-> 3162     mimage._draw_list_compositing_images(
   3163         renderer, self, artists, self.suppressComposite)
   3165     renderer.close_group('figure')
   3166 finally:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/image.py:132, in _draw_list_compositing_images(renderer, parent, artists, suppress_composite)
    130 if not_composite or not has_images:
    131     for a in artists:
--> 132         a.draw(renderer)
    133 else:
    134     # Composite any adjacent images together
    135     image_group = []

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/artist.py:72, in allow_rasterization.<locals>.draw_wrapper(artist, renderer)
     69     if artist.get_agg_filter() is not None:
     70         renderer.start_filter()
---> 72     return draw(artist, renderer)
     73 finally:
     74     if artist.get_agg_filter() is not None:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axes/_base.py:3101, in _AxesBase.draw(self, renderer)
   3098     for spine in self.spines.values():
   3099         artists.remove(spine)
-> 3101 self._update_title_position(renderer)
   3103 if not self.axison:
   3104     for _axis in self._axis_map.values():

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axes/_base.py:3036, in _AxesBase._update_title_position(self, renderer)
   3033 bb = None
   3034 if (ax.xaxis.get_ticks_position() in ['top', 'unknown']
   3035         or ax.xaxis.get_label_position() == 'top'):
-> 3036     bb = ax.xaxis.get_tightbbox(renderer)
   3037 if bb is None:
   3038     if 'outline' in ax.spines:
   3039         # Special case for colorbars:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axis.py:1372, in Axis.get_tightbbox(self, renderer, for_layout_only)
   1369     renderer = self.figure._get_renderer()
   1370 ticks_to_draw = self._update_ticks()
-> 1372 self._update_label_position(renderer)
   1374 # go back to just this axis's tick labels
   1375 tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axis.py:2413, in XAxis._update_label_position(self, renderer)
   2409     return
   2411 # get bounding boxes for this axis and any siblings
   2412 # that have been set by `fig.align_xlabels()`
-> 2413 bboxes, bboxes2 = self._get_tick_boxes_siblings(renderer=renderer)
   2415 x, y = self.label.get_position()
   2416 if self.label_position == 'bottom':

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axis.py:2206, in Axis._get_tick_boxes_siblings(self, renderer)
   2204 axis = ax._axis_map[name]
   2205 ticks_to_draw = axis._update_ticks()
-> 2206 tlb, tlb2 = axis._get_ticklabel_bboxes(ticks_to_draw, renderer)
   2207 bboxes.extend(tlb)
   2208 bboxes2.extend(tlb2)

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axis.py:1351, in Axis._get_ticklabel_bboxes(self, ticks, renderer)
   1349 if renderer is None:
   1350     renderer = self.figure._get_renderer()
-> 1351 return ([tick.label1.get_window_extent(renderer)
   1352          for tick in ticks if tick.label1.get_visible()],
   1353         [tick.label2.get_window_extent(renderer)
   1354          for tick in ticks if tick.label2.get_visible()])

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/axis.py:1351, in <listcomp>(.0)
   1349 if renderer is None:
   1350     renderer = self.figure._get_renderer()
-> 1351 return ([tick.label1.get_window_extent(renderer)
   1352          for tick in ticks if tick.label1.get_visible()],
   1353         [tick.label2.get_window_extent(renderer)
   1354          for tick in ticks if tick.label2.get_visible()])

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/text.py:959, in Text.get_window_extent(self, renderer, dpi)
    954     raise RuntimeError(
    955         "Cannot get window extent of text w/o renderer. You likely "
    956         "want to call 'figure.draw_without_rendering()' first.")
    958 with cbook._setattr_cm(self.figure, dpi=dpi):
--> 959     bbox, info, descent = self._get_layout(self._renderer)
    960     x, y = self.get_unitless_position()
    961     x, y = self.get_transform().transform((x, y))

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/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, dpi=self.figure.dpi)
    376 min_dy = (lp_h - lp_d) * self._linespacing
    378 for i, line in enumerate(lines):

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/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/3.9.20/x64/lib/python3.9/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/3.9.20/x64/lib/python3.9/site-packages/matplotlib/backends/backend_agg.py:212, in RendererAgg.get_text_width_height_descent(self, s, prop, ismath)
    210 _api.check_in_list(["TeX", True, False], ismath=ismath)
    211 if ismath == "TeX":
--> 212     return super().get_text_width_height_descent(s, prop, ismath)
    214 if ismath:
    215     ox, oy, width, height, descent, font_image = \
    216         self.mathtext_parser.parse(s, self.dpi, prop)

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/backend_bases.py:597, in RendererBase.get_text_width_height_descent(self, s, prop, ismath)
    593 fontsize = prop.get_size_in_points()
    595 if ismath == 'TeX':
    596     # todo: handle properties
--> 597     return self.get_texmanager().get_text_width_height_descent(
    598         s, fontsize, renderer=self)
    600 dpi = self.points_to_pixels(72)
    601 if ismath:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/texmanager.py:363, in TexManager.get_text_width_height_descent(cls, tex, fontsize, renderer)
    361 if tex.strip() == '':
    362     return 0, 0, 0
--> 363 dvifile = cls.make_dvi(tex, fontsize)
    364 dpi_fraction = renderer.points_to_pixels(1.) if renderer else 1
    365 with dviread.Dvi(dvifile, 72 * dpi_fraction) as dvi:

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/texmanager.py:295, in TexManager.make_dvi(cls, tex, fontsize)
    293     with TemporaryDirectory(dir=cwd) as tmpdir:
    294         tmppath = Path(tmpdir)
--> 295         cls._run_checked_subprocess(
    296             ["latex", "-interaction=nonstopmode", "--halt-on-error",
    297              f"--output-directory={tmppath.name}",
    298              f"{texfile.name}"], tex, cwd=cwd)
    299         (tmppath / Path(dvifile).name).replace(dvifile)
    300 return dvifile

File /opt/hostedtoolcache/Python/3.9.20/x64/lib/python3.9/site-packages/matplotlib/texmanager.py:254, in TexManager._run_checked_subprocess(cls, command, tex, cwd)
    250     report = subprocess.check_output(
    251         command, cwd=cwd if cwd is not None else cls._texcache,
    252         stderr=subprocess.STDOUT)
    253 except FileNotFoundError as exc:
--> 254     raise RuntimeError(
    255         f'Failed to process string with tex because {command[0]} '
    256         'could not be found') from exc
    257 except subprocess.CalledProcessError as exc:
    258     raise RuntimeError(
    259         '{prog} was not able to process the following string:\n'
    260         '{tex!r}\n\n'
   (...)
    267             exc=exc.output.decode('utf-8', 'backslashreplace'))
    268         ) from None

RuntimeError: Failed to process string with tex because latex could not be found
<Figure size 800x600 with 1 Axes>