Conociendo nuestros datos de pingüinos. 🗺🧭🐧
Instalar librerías necesarias
Importar librerías
import empiricaldist
import janitor
import matplotlib.pyplot as plt
import numpy as np
import palmerpenguins
import pandas as pd
import scipy.stats
import seaborn as sns
import sklearn.metrics
import statsmodels.api as sm
import statsmodels.formula.api as smf
import statsmodels.stats as ss
import session_info
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Establecer apariencia general de los gráficos
%matplotlib inline
sns.set_style(style='whitegrid')
sns.set_context(context='notebook')
plt.rcParams['figure.figsize'] = (11, 9.4)
penguin_color = {
'Adelie': '#ff6602ff',
'Gentoo': '#0f7175ff',
'Chinstrap': '#c65dc9ff'
}
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Cargar los datos
Utilizando el paquete palmerpenguins
Datos crudos
palmerpenguins.load_pen
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Datos previamente procesados
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Utilizando los conjuntos de datos de seaborn
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Utilizando la interfaz de Deepnote
Links de importación de datos:
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preprocessed_penguins_df2 = pd.read_csv('penguins.csv')
preprocessed_penguins_df2
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Colecta y validación de datos
¿Qué tipo de dato son las variables del conjunto de datos?
preprocessed_penguins_df.dtypes
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¿Cuántas variables de cada tipo de dato tenemos en el conjunto de datos?
(
preprocessed_penguins_df
.dtypes
.value_counts()
)
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¿Cuántas variables y observaciones tenemos en el conjunto de datos?
preprocessed_penguins_df.shape
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¿Existen valores nulos explicitos en el conjunto de datos?
(
preprocessed_penguins_df
.isnull()
.any()
)
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De tener observaciones con valores nulos, ¿cuántas tenemos por cada variable?
(
preprocessed_penguins_df
.isnull()
.sum()
.sort_values(ascending=False)
)
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¿Cuántos valores nulos tenemos en total en el conjunto de datos?
(
preprocessed_penguins_df
.isnull()
.sum()
.sum()
)
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¿Cuál es la proporción de valores nulos por cada variable?
(
preprocessed_penguins_df
.isnull()
.melt(value_name='missing')
.pipe(
lambda df: (
sns.displot(
data=df,
y='variable',
hue='missing',
multiple='fill',
aspect=2
)
)
)
)
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¿Cómo podemos visualizar los valores nulos en todo el conjunto de datos?
(
preprocessed_penguins_df
.isnull()
.transpose()
.pipe(
lambda df: sns.heatmap(data=df)
)
)
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¿Cuántas observaciones perdemos si eliminamos los datos faltantes?
processed_penguins_df = (
preprocessed_penguins_df
.dropna()
)
processed_penguins_df
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Conteos y proporciones
Preludio: ¿Qué estadísticos describen el conjunto de datos?
Todas las variables
processed_penguins_df.describe(include='all')
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Solo las numéricas
processed_penguins_df.describe(include=[np.number])
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Solo categóricas - 1
processed_penguins_df.describe(include=object)
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Solo categóricas - 2
(
processed_penguins_df
.astype(
{
'species': 'category',
'island': 'category',
'sex': 'category'
}
)
.describe(include=['category', object])
)
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¿Cómo visualizar los conteos?
Pandas
(
processed_penguins_df
.species
.value_counts()
.plot(
kind='bar',
# color=penguin_color.values()
)
)
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Seaborn
sns.catplot(
data=processed_penguins_df,
x='species',
kind='count',
palette=penguin_color,
# order=processed_penguins_df.value_counts('species', sort=True).index
)
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(
processed_penguins_df
.value_counts('species', sort=True)
.reset_index(name='count')
.pipe(
lambda df: (
sns.barplot(
data=df,
x='species',
y='count',
palette=penguin_color
)
)
)
)
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¿Cómo visualizar las proporciones?
(
processed_penguins_df
.add_column('variable', '')
.pipe(
lambda df: (
sns.displot(
data=df,
x='variable',
hue='species',
multiple='fill',
palette=penguin_color
)
)
)
)
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Medidas de tendencia central
Media o promedio
processed_penguins_df.bill_depth_mm.mean()
np.mean(processed_penguins_df.bill_depth_mm)
processed_penguins_df.mean()
processed_penguins_df.median()
processed_penguins_df.mode()
processed_penguins_df.describe(include=object)
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np.mean(processed_penguins_df.bill_depth_mm)
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processed_penguins_df.mean()
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Mediana
processed_penguins_df.median()
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Moda
processed_penguins_df.mode()
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processed_penguins_df.describe(include=object)
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Medidas de dispersión
¿Cuál es el valor máximo de las variables?
processed_penguins_df.max()
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¿Cuál es el valor mínimo de las variables?
processed_penguins_df.min()
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¿Cuál es el rango de las variables?
processed_penguins_df.max(numeric_only=True) - processed_penguins_df.min(numeric_only=True)
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¿Cuál es la desviación estándar de las variables?
processed_penguins_df.std()
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¿Cuál es el rango intercuartílico?
processed_penguins_df.quantile(0.25)
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processed_penguins_df.quantile(0.75) - processed_penguins_df.quantile(0.25)
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(
processed_penguins_df
.quantile(q=[0.75, 0.50, 0.25])
.transpose()
.rename_axis('metric')
.reset_index()
.assign(
iqr = lambda df: df[0.75] - df[0.25]
)
)
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¿Cómo puedo visualizar la distribución de una variable?
Histograma
sns.histplot(
data=processed_penguins_df,
x='flipper_length_mm',
)
plt.axvline(
x=processed_penguins_df.flipper_length_mm.mean(),
color='red',
linestyle='dashed',
linewidth=2
)
plt.axvline(
x=processed_penguins_df.flipper_length_mm.median(),
color='blue',
linestyle='dashed',
linewidth=2
)
plt.axvline(
x=processed_penguins_df.flipper_length_mm.mode().values[0],
color='black',
linestyle='dashed',
linewidth=4
)
plt.axvline(
x=processed_penguins_df.flipper_length_mm.quantile(0.25),
color='yellow',
linestyle='dashed',
linewidth=2
)
plt.axvline(
x=processed_penguins_df.flipper_length_mm.quantile(0.75),
color='yellow',
linestyle='dashed',
linewidth=2
)
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Diagrama de caja / boxplot
sns.boxplot(
x=processed_penguins_df.flipper_length_mm,
)
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Limitaciones
def freedman_diaconis_bindwidth(x: pd.Series) -> float:
"""Find optimal bindwidth using Freedman-Diaconis rule."""
IQR = x.quantile(0.75) - x.quantile(0.25)
N = x.size
return 2 * IQR / N ** (1 / 3)
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sns.histplot(
data=processed_penguins_df,
x='flipper_length_mm',
binwidth=6.3
)
plt.axvline(
x=processed_penguins_df.flipper_length_mm.mean(),
color='red',
linestyle='dashed',
linewidth=2
)
plt.axvline(
x=processed_penguins_df.flipper_length_mm.median(),
color='blue',
linestyle='dashed',
linewidth=2
)
plt.axvline(
x=processed_penguins_df.flipper_length_mm.mode().values[0],
color='black',
linestyle='dashed',
linewidth=4
)
plt.axvline(
x=processed_penguins_df.flipper_length_mm.quantile(0.25),
color='yellow',
linestyle='dashed',
linewidth=2
)
plt.axvline(
x=processed_penguins_df.flipper_length_mm.quantile(0.75),
color='yellow',
linestyle='dashed',
linewidth=2
)
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Distribuciones: PMFs, CDFs y PDFs
Funciones de probabilidad de masas (PMFs)
Utilizando seaborn
sns.histplot(
data=processed_penguins_df,
x='flipper_length_mm',
binwidth=1,
stat='probability'
)
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Utilizando empiricaldist
pmf_flipper_length_mm = empiricaldist.Pmf.from_seq(
processed_penguins_df.flipper_length_mm,
normalize=True
)
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pmf_flipper_length_mm.bar()
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pmf_flipper_length_mm(231)
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processed_penguins_df.flipper_length_mm.max()
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Funciones empirícas de probabilidad acumulada (ECDFs)
Utilizando seaborn
sns.ecdfplot(
data=processed_penguins_df,
x="flipper_length_mm"
)
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Utilizando empiricaldist
cdf_flipper_length_mm = empiricaldist.Cdf.from_seq(
processed_penguins_df.flipper_length_mm,
normalize=True
)
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cdf_flipper_length_mm.plot()
q = 200 # Specify quantity
p = cdf_flipper_length_mm.forward(q)
plt.vlines(
x=q,
ymin=0,
ymax=p,
color = 'black',
linestyle='dashed'
)
plt.hlines(
y=p,
xmin=pmf_flipper_length_mm.qs[0],
xmax=q,
color='black',
linestyle='dashed'
)
plt.plot(q, p, 'ro')
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cdf_flipper_length_mm.step()
p_1 = 0.25 # Specify probability
p_2 = 0.75
ps = (0.25, 0.75) # IQR
qs = cdf_flipper_length_mm.inverse(ps)
plt.vlines(
x=qs,
ymin=0,
ymax=ps,
color = 'black',
linestyle='dashed'
)
plt.hlines(
y=ps,
xmin=pmf_flipper_length_mm.qs[0],
xmax=qs,
color='black',
linestyle='dashed'
)
plt.scatter(
x=qs,
y=ps,
color='red',
zorder=2
)
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Comparando distribuciones
sns.ecdfplot(
data=processed_penguins_df,
x='flipper_length_mm',
hue='species',
palette=penguin_color
)
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Funciones de densidad de probabilidad
sns.kdeplot(
data=processed_penguins_df,
x='flipper_length_mm',
bw_method=0.1
)
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stats = processed_penguins_df.body_mass_g.describe()
stats
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np.random.seed(42)
xs = np.linspace(stats['min'], stats['max'])
ys = scipy.stats.norm(stats['mean'], stats['std']).cdf(xs)
plt.plot(xs, ys, color='black', linestyle='dashed')
empiricaldist.Cdf.from_seq(
processed_penguins_df.body_mass_g,
normalize=True
).plot()
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xs = np.linspace(stats['min']-1000, stats['max'] + 1000)
ys = scipy.stats.norm(stats['mean'], stats['std']).pdf(xs)
plt.plot(xs, ys, color='black', linestyle='dashed')
sns.kdeplot(
data=processed_penguins_df,
x='body_mass_g'
)
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Ley de los Grandes Números y Teorema del Límite Central
Ley de los Grandes Números
dice = empiricaldist.Pmf.from_seq([1, 2, 3, 4, 5, 6])
dice.bar()
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for sample_size in (1e2, 1e3, 1e4):
sample_size = int(sample_size)
values = dice.sample(sample_size)
sample_pmf = empiricaldist.Pmf.from_seq(values)
plt.figure(figsize=(5,5))
sample_pmf.bar()
plt.axhline(y=1/6, color = 'red', linestyle='dashed')
plt.ylim([0, 0.50])
plt.title(f"Sample size: {sample_size}")
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Teorema del límite central
processed_penguins_df.sex.value_counts(normalize=True)
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sex_numeric = processed_penguins_df.sex.replace(['Male', 'Female'], [1, 0])
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number_samples = 1000
sample_size=35
samples_df = pd.DataFrame()
np.random.seed(42)
for i in range(1, number_samples + 1):
sex_numeric_sample = sex_numeric.sample(sample_size, replace=True).to_numpy()
sample_name = f"sample_{i}"
samples_df[sample_name] = sex_numeric_sample
male_population_mean = samples_df.mean().mean()
print(f"Estimated percentage of male penguins in population is: {male_population_mean * 100:.4f}%")
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sample_means_binomial = pd.DataFrame(samples_df.mean(), columns=['sample_mean'])
sns.kdeplot(data=sample_means_binomial)
plt.axvline(x=sex_numeric.mean(), color='red', linestyle='dashed')
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sample_size_experiment = pd.DataFrame(
[[i, samples_df.iloc[:, 0:i].mean().mean().mean()] for i in range(1, number_samples + 1)],
columns=['sample_size', 'estimated_mean']
)
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sns.scatterplot(
data=sample_size_experiment,
x='sample_size',
y='estimated_mean'
)
plt.axhline(
y=sex_numeric.mean(),
color='red',
linestyle='dashed'
)
plt.ylim([sex_numeric.mean() - 0.20, sex_numeric.mean() + 0.20])
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Estableciendo relaciones: Gráfica de puntos
sns.scatterplot(
data=processed_penguins_df,
x='bill_length_mm',
y='bill_depth_mm',
alpha=1/2,
s=100
)
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sns.displot(
data=processed_penguins_df,
x='bill_length_mm',
y='bill_depth_mm',
rug=True
)
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sns.displot(
data=processed_penguins_df,
x='bill_length_mm',
y='bill_depth_mm',
kind='kde',
rug=True
)
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sns.jointplot(
data=processed_penguins_df,
x='bill_length_mm',
y='bill_depth_mm',
marginal_kws=dict(bins=25, fill=False)
)
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Estableciendo relaciones: Gráficos de violín y boxplots
sns.scatterplot(
data=processed_penguins_df,
x='species',
y='flipper_length_mm',
hue='species',
palette=penguin_color
)
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sns.stripplot(
data=processed_penguins_df,
x='species',
y='flipper_length_mm',
palette=penguin_color
)
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ax = sns.boxplot(
data=processed_penguins_df,
x='flipper_length_mm',
y='species',
palette=penguin_color,
whis=np.inf
)
ax = sns.stripplot(
data=processed_penguins_df,
x='flipper_length_mm',
y='species',
color='.3'
)
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ax = sns.violinplot(
data=processed_penguins_df,
x='species',
y='flipper_length_mm',
color='.8'
)
ax = sns.stripplot(
data=processed_penguins_df,
x='species',
y='flipper_length_mm',
palette=penguin_color
)
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sns.swarmplot(
data=processed_penguins_df,
x='species',
y='flipper_length_mm',
hue='species',
palette=penguin_color
)
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Estableciendo relaciones: Matrices de correlación
¿Existe una correlación lineal entre alguna de nuestras variables?
processed_penguins_df.corr()
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¿Como puedo visualizar los coeficientes de correlación?
sns.heatmap(
data=processed_penguins_df.corr(),
cmap=sns.diverging_palette(20, 230, as_cmap=True),
center=0,
vmin=-1,
vmax=1,
linewidths=0.5,
cbar_kws={"shrink": 0.5},
annot=True
)
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sns.clustermap(
data=processed_penguins_df.corr(),
cmap= sns.diverging_palette(20, 230, as_cmap=True), # 'BrBG'
center=0,
vmin=-1,
vmax=1,
linewidths=0.5,
cbar_kws={"shrink": 0.5},
annot=True
)
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¿Cómo podría representar una variable categórica como numérica discreta?
processed_penguins_df = (
processed_penguins_df
.assign(
numeric_sex=lambda df: df.sex.replace(['Female', 'Male'], [0, 1])
)
)
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sns.clustermap(
data=processed_penguins_df.corr(),
cmap= sns.diverging_palette(20, 230, as_cmap=True), # 'BrBG'
center=0,
vmin=-1,
vmax=1,
linewidths=0.5,
cbar_kws={"shrink": 0.5},
annot=True
)
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¿Cuál es una límitante de los coeficientes de correlación lineal?
Sólo nos ayuda a determinar la posible existencia de una correlación lineal, sin embargo, su ausencia no significa que no exista otro tipo de correlación
x = np.linspace(-100, 100, 100)
y = x ** 2
y += np.random.normal(0, 1000, x.size)
sns.scatterplot(x=x, y=y)
np.corrcoef(x, y)
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x = np.linspace(-100, 100, 100)
y = x ** 3
y += np.random.normal(0, 1000, x.size)
sns.scatterplot(x=x, y=y)
np.corrcoef(x, y)
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sns.scatterplot(
data=processed_penguins_df,
x='bill_length_mm',
y='bill_depth_mm'
)
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El coeficiente de correlación no nos habla del impacto de la relación
np.random.seed(42)
x_1 = np.linspace(0, 100, 100)
y_1 = 0.1 * x_1 + 3 + np.random.uniform(-2, 2, size=x_1.size)
sns.scatterplot(
x=x_1,
y=y_1
)
x_2 = np.linspace(0, 100, 100)
y_2 = 0.5 * x_2 + 1 + np.random.uniform(0, 60, size=x_2.size)
sns.scatterplot(
x=x_2,
y=y_2
)
plt.legend(labels=['1', '2'])
print(np.corrcoef(x_1, y_1))
print(np.corrcoef(x_2, y_2))
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Estableciendo relaciones: Análisis de regresión simple
res_1 = scipy.stats.linregress(x=x_1, y=y_1)
res_2 = scipy.stats.linregress(x=x_2, y=y_2)
print(res_1, res_2, sep="\n")
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sns.scatterplot(
x=x_1,
y=y_1
)
fx_1 = np.array([x_1.min(), x_1.max()])
fy_1 = res_1.intercept + res_1.slope * fx_1
plt.plot(fx_1, fy_1)
sns.scatterplot(
x=x_2,
y=y_2
)
fx_2 = np.array([x_2.min(), x_2.max()])
fy_2 = res_2.intercept + res_2.slope * fx_2
plt.plot(fx_2, fy_2)
plt.legend(labels=['1', '1', '2', '2'])
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sns.scatterplot(
data=processed_penguins_df,
x='bill_length_mm',
y='bill_depth_mm'
)
res_penguins = scipy.stats.linregress(x=processed_penguins_df.bill_length_mm, y=processed_penguins_df.bill_depth_mm)
print(res_penguins)
fx_1 = np.array([processed_penguins_df.bill_length_mm.min(), processed_penguins_df.bill_length_mm.max()])
fy_1 = res_penguins.intercept + res_penguins.slope * fx_1
plt.plot(fx_1, fy_1)
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sns.lmplot(
data=processed_penguins_df,
x='bill_length_mm',
y='bill_depth_mm',
height=10
)
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Limitaciones del análisis de regresión simple
La regresión lineal simple no es simétrica
x = processed_penguins_df.bill_length_mm
y = processed_penguins_df.bill_depth_mm
res_x_y = scipy.stats.linregress(x=x, y=y)
res_y_x = scipy.stats.linregress(y=x, x=y)
print(res_x_y, res_y_x, sep="\n")
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sns.scatterplot(
x=x,
y=y
)
fx_1 = np.array([x.min(), x.max()])
fy_1 = res_x_y.intercept + res_x_y.slope * fx_1
plt.plot(fx_1, fy_1)
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sns.scatterplot(
x=y,
y=x
)
fx_1 = np.array([y.min(), y.max()])
fy_1 = res_y_x.intercept + res_y_x.slope * fx_1
plt.plot(fx_1, fy_1)
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La regresión no nos dice nada sobre la causalidad, pero existen herramientas para separar las relaciones entre varias variables
La pendiente es -0.634905, lo que significa que cada milímetro adicional de profundidad del pico es asociado a un decremento de -0.634905 milímetros de la longitud del pico de un pingüino.
(
smf.ols(
formula="bill_length_mm ~ bill_depth_mm",
data=processed_penguins_df
)
.fit()
.params
)
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(
smf.ols(
formula="bill_depth_mm ~ bill_length_mm",
data=processed_penguins_df
)
.fit()
.summary()
)
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Análisis de regresión múltiple
Olvidé mi báscula para pesar a los pingüinos, ¿Cuál sería la mejor forma de capturar ese dato?
Creando modelos
model_1 = (
smf.ols(
formula="body_mass_g ~ bill_length_mm",
data=processed_penguins_df
)
.fit()
)
model_1.summary()
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model_2 = (
smf.ols(
formula="body_mass_g ~ bill_length_mm + bill_depth_mm ",
data=processed_penguins_df
)
.fit()
)
model_2.summary()
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model_3 = (
smf.ols(
formula="body_mass_g ~ bill_length_mm + bill_depth_mm + flipper_length_mm",
data=processed_penguins_df
)
.fit()
)
model_3.summary()
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model_4 = (
smf.ols(
formula="body_mass_g ~ bill_length_mm + bill_depth_mm + flipper_length_mm + C(sex)",
data=processed_penguins_df
)
.fit()
)
model_4.summary()
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model_5 = (
smf.ols(
formula="body_mass_g ~ flipper_length_mm + C(sex)",
data=processed_penguins_df
)
.fit()
)
model_5.summary()
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Visualizando resultados
models_results = pd.DataFrame(
dict(
actual_value=processed_penguins_df.body_mass_g,
prediction_model_1 = model_1.predict(),
prediction_model_2 = model_2.predict(),
prediction_model_3 = model_3.predict(),
prediction_model_4 = model_4.predict(),
prediction_model_5 = model_5.predict(),
species=processed_penguins_df.species,
sex=processed_penguins_df.sex
)
)
models_results
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sns.ecdfplot(
data=models_results#.select_columns(['actual_value', 'prediction_model_5'])
)
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sns.kdeplot(
data=models_results,
cumulative=False
)
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sns.lmplot(
data=processed_penguins_df,
x='flipper_length_mm',
y='body_mass_g',
height=10,
hue='sex'
)
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Análisis de regresión logística
smf.logit(
formula='sex_numeric ~ flipper_length_mm + bill_length_mm + bill_depth_mm + C(island)',
data=processed_penguins_df
).fit().summary()
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(
processed_penguins_df
.value_counts(['island', 'sex', 'species'])
.reset_index(name='count')
)
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processed_penguins_df.species.unique()
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processed_penguins_df = (
processed_penguins_df
.assign(is_adelie=lambda df: df.species.replace(['Adelie', 'Chinstrap', 'Gentoo'], [1, 0, 0]))
)
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model_is_adelie = smf.logit(
formula='is_adelie ~ flipper_length_mm + C(sex)',
data=processed_penguins_df
).fit(maxiter=100)
model_is_adelie.params
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is_adelie_df_predictions = pd.DataFrame(
dict(
actual_adelie = processed_penguins_df.species.replace(['Adelie', 'Chinstrap', 'Gentoo'], [1, 0, 0]),
predicted_values = model_is_adelie.predict().round()
)
)
is_adelie_df_predictions
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(
is_adelie_df_predictions
.value_counts(['actual_adelie', 'predicted_values'])
.reset_index(name='count')
.pivot_wider(
index='actual_adelie',
names_from='predicted_values',
values_from='count'
)
.rename_column('actual_adelie', 'actual / predicted')
)
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print(
sklearn.metrics.confusion_matrix(
is_adelie_df_predictions.actual_adelie,
is_adelie_df_predictions.predicted_values
)
)
sklearn.metrics.accuracy_score(
is_adelie_df_predictions.actual_adelie,
is_adelie_df_predictions.predicted_values
)
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Paradoja de Simpson
sns.scatterplot(
data=processed_penguins_df,
x='bill_length_mm',
y='bill_depth_mm'
)
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sns.regplot(
data=processed_penguins_df,
x='bill_length_mm',
y='bill_depth_mm'
)
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sns.lmplot(
data=processed_penguins_df,
x='bill_length_mm',
y='bill_depth_mm',
hue='species',
height=10,
palette=penguin_color
)
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sns.pairplot(data=processed_penguins_df, hue='species', palette=penguin_color)
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Información de sesión
session_info.show()
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