import pandas as pd
df = pd.read_excel('uschange.xlsx' )
df.Consumption.plot(legend=True )
df.Income.plot(legend=True )
from statsmodels.formula.api import ols
ols('Consumption ~ Income' , df).fit().summary()
OLS Regression Results Dep. Variable: Consumption R-squared: 0.159 Model: OLS Adj. R-squared: 0.154 Method: Least Squares F-statistic: 34.98 Date: Sun, 28 May 2023 Prob (F-statistic): 1.58e-08 Time: 11:10:33 Log-Likelihood: -169.62 No. Observations: 187 AIC: 343.2 Df Residuals: 185 BIC: 349.7 Df Model: 1 Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975] Intercept 0.5451 0.056 9.789 0.000 0.435 0.655 Income 0.2806 0.047 5.915 0.000 0.187 0.374
Omnibus: 16.528 Durbin-Watson: 1.696 Prob(Omnibus): 0.000 Jarque-Bera (JB): 29.145 Skew: -0.454 Prob(JB): 4.69e-07 Kurtosis: 4.707 Cond. No. 2.08
m = ols('Consumption ~ Income + Production + Unemployment + Savings' , df).fit()
m.summary()
OLS Regression Results Dep. Variable: Consumption R-squared: 0.754 Model: OLS Adj. R-squared: 0.749 Method: Least Squares F-statistic: 139.5 Date: Sun, 28 May 2023 Prob (F-statistic): 2.62e-54 Time: 11:10:34 Log-Likelihood: -54.692 No. Observations: 187 AIC: 119.4 Df Residuals: 182 BIC: 135.5 Df Model: 4 Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975] Intercept 0.2673 0.037 7.184 0.000 0.194 0.341 Income 0.7145 0.042 16.934 0.000 0.631 0.798 Production 0.0459 0.026 1.773 0.078 -0.005 0.097 Unemployment -0.2048 0.106 -1.941 0.054 -0.413 0.003 Savings -0.0453 0.003 -16.287 0.000 -0.051 -0.040
Omnibus: 18.566 Durbin-Watson: 2.169 Prob(Omnibus): 0.000 Jarque-Bera (JB): 28.796 Skew: 0.564 Prob(JB): 5.58e-07 Kurtosis: 4.556 Cond. No. 61.9
y_pred = m.predict(df)
df.Consumption.plot(legend=True )
y_pred.plot(legend=True , label='prediction' )
import matplotlib.pyplot as plt
import numpy as np
plt.plot(df.Consumption, y_pred, '.' )
x = np.array(plt.gca().get_xlim())
plt.plot(x, x, '--' )
[<matplotlib.lines.Line2D at 0x158d851a290>]
0 0.168638
1 -0.184591
2 -0.051472
3 -0.070916
4 0.267760
...
182 -0.109993
183 -0.037906
184 -0.113017
185 0.128985
186 -0.046047
Length: 187, dtype: float64
0 0.168638
1 -0.184591
2 -0.051472
3 -0.070916
4 0.267760
...
182 -0.109993
183 -0.037906
184 -0.113017
185 0.128985
186 -0.046047
Length: 187, dtype: float64
from statsmodels.graphics.tsaplots import plot_acf
plot_acf(m.resid);
import pingouin as pg
pg.corr(df.Income, m.resid)
n r CI95% p-val BF10 power pearson 187 -1.283695e-15 [-0.14, 0.14] 1.0 0.092 0.049914
n r CI95% p-val BF10 power pearson 187 3.885781e-16 [-0.14, 0.14] 1.0 0.092 0.049914
n = len (df)
df['t' ] = np.arange(n)
ols('Consumption ~ t' , df).fit().summary()
OLS Regression Results Dep. Variable: Consumption R-squared: 0.025 Model: OLS Adj. R-squared: 0.020 Method: Least Squares F-statistic: 4.726 Date: Sun, 28 May 2023 Prob (F-statistic): 0.0310 Time: 11:12:40 Log-Likelihood: -183.46 No. Observations: 187 AIC: 370.9 Df Residuals: 185 BIC: 377.4 Df Model: 1 Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975] Intercept 0.9242 0.095 9.777 0.000 0.738 1.111 t -0.0019 0.001 -2.174 0.031 -0.004 -0.000
Omnibus: 46.181 Durbin-Watson: 1.333 Prob(Omnibus): 0.000 Jarque-Bera (JB): 115.917 Skew: -1.058 Prob(JB): 6.74e-26 Kurtosis: 6.225 Cond. No. 214.
r = (n + 1 ) // 4
df['season' ] = np.tile([1 , 2 , 3 , 4 ], r)[:187 ]
ols('Consumption ~ C(season)' , df).fit().summary()
OLS Regression Results Dep. Variable: Consumption R-squared: 0.009 Model: OLS Adj. R-squared: -0.007 Method: Least Squares F-statistic: 0.5513 Date: Sun, 28 May 2023 Prob (F-statistic): 0.648 Time: 11:13:05 Log-Likelihood: -184.97 No. Observations: 187 AIC: 377.9 Df Residuals: 183 BIC: 390.9 Df Model: 3 Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975] Intercept 0.7356 0.096 7.667 0.000 0.546 0.925 C(season)[T.2] -0.0296 0.136 -0.218 0.828 -0.297 0.238 C(season)[T.3] 0.1143 0.136 0.842 0.401 -0.153 0.382 C(season)[T.4] -0.0424 0.136 -0.311 0.756 -0.312 0.227
Omnibus: 29.475 Durbin-Watson: 1.283 Prob(Omnibus): 0.000 Jarque-Bera (JB): 63.812 Skew: -0.718 Prob(JB): 1.39e-14 Kurtosis: 5.476 Cond. No. 4.78
