In [1]:

import pandas as pd                         
import statsmodels.api as sm               
import statsmodels.formula.api as smf      
import matplotlib.pyplot as plt 

#Link de Interés: https://www.statsmodels.org/devel/

/usr/local/lib/python3.7/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.
  import pandas.util.testing as tm

statsmodels es un módulo de Python que proporciona clases y funciones para la estimación de muchos modelos estadísticos diferentes, así como para realizar pruebas estadísticas y exploración de datos estadísticos.

In [2]:

#Carga de datos
file = 'https://raw.githubusercontent.com/fhernanb/Python-para-estadistica/master/03%20Regression/Regresi%C3%B3n%20lineal%20simple/softdrink.csv'
df = pd.read_csv(file)

In [3]:

#Vemos nuestros datos
df.head()   

Out[3]:

	Obs	y	x1	x2
0	1	16.68	7	560
1	2	11.50	3	220
2	3	12.03	3	340
3	4	14.88	4	80
4	5	13.75	6	150

In [4]:

#Scatterplot
df.plot(kind='scatter', x='x1', y='y')

Out[4]:

<matplotlib.axes._subplots.AxesSubplot at 0x7f15b14a9710>

In [5]:

#Creacion del modelo con statsmodels.api.

X = df["x1"] # X: variables independientes
X = sm.add_constant(X)# Se agrega una intercepción (beta_0) al modelo
y = df["y"] # Y: variable respuesta (o variable dependiente)

# Fiteamos el modelo
mod1 = sm.OLS(y, X).fit()   
predictions = mod1.predict(X)

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/tsatools.py:117: FutureWarning: In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only
  x = pd.concat(x[::order], 1)

In [6]:

#Estadisticas del modelo
mod1.summary()   

Out[6]:

OLS Regression Results
Dep. Variable:	y	R-squared:	0.930
Model:	OLS	Adj. R-squared:	0.927
Method:	Least Squares	F-statistic:	307.8
Date:	Sun, 08 May 2022	Prob (F-statistic):	8.22e-15
Time:	14:14:12	Log-Likelihood:	-70.197
No. Observations:	25	AIC:	144.4
Df Residuals:	23	BIC:	146.8
Df Model:	1
Covariance Type:	nonrobust

	coef	std err	t	P>\|t\|	[0.025	0.975]
const	3.3208	1.371	2.422	0.024	0.484	6.157
x1	2.1762	0.124	17.546	0.000	1.920	2.433

Omnibus:	2.383	Durbin-Watson:	0.946
Prob(Omnibus):	0.304	Jarque-Bera (JB):	1.037
Skew:	0.388	Prob(JB):	0.595
Kurtosis:	3.627	Cond. No.	18.2

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

In [7]:

#Ajuste del modelo - statsmodels.formula.api
mod2 = smf.ols('y ~ x1', data=df).fit()

In [8]:

#Vemos las estadisticas del modelo
print(mod2.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                      y   R-squared:                       0.930
Model:                            OLS   Adj. R-squared:                  0.927
Method:                 Least Squares   F-statistic:                     307.8
Date:                Sun, 08 May 2022   Prob (F-statistic):           8.22e-15
Time:                        14:14:15   Log-Likelihood:                -70.197
No. Observations:                  25   AIC:                             144.4
Df Residuals:                      23   BIC:                             146.8
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept      3.3208      1.371      2.422      0.024       0.484       6.157
x1             2.1762      0.124     17.546      0.000       1.920       2.433
==============================================================================
Omnibus:                        2.383   Durbin-Watson:                   0.946
Prob(Omnibus):                  0.304   Jarque-Bera (JB):                1.037
Skew:                           0.388   Prob(JB):                        0.595
Kurtosis:                       3.627   Cond. No.                         18.2
==============================================================================

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

In [9]:

#Recta de regresion estimada
fig, ax = plt.subplots(figsize=(8,6))                                    # Ajuste del gráfico
ax.plot(df["x1"] , df["y"] , 'o', label="Datos")                         # Ajuste para las etiquetas del gráfico
ax.plot(df["x1"], mod2.fittedvalues, 'r--.', label="Ajustado")           # Ajuste para las etiquetas del gráfico
legend = ax.legend(loc="best")                                           # Ajustes para las leyendas del gráfico
plt.xlabel('Cantidad de cajas')                                          # Etiqueta del eje X
plt.ylabel('Tiempo (min)')                                               # Etiqueta del eje Y
plt.title('Diagrama de dispersión con la recta del modelo ajustado');    # Título del gráfico

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