P Value

When you perform a hypothesis test in statistics, a p-value helps you determine the significance of your results.

  • A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

  • A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

  • p-values very close to the cutoff (0.05) are considered to be marginal (could go either way). Always report the p-value so your readers can draw their own conclusions.


import matplotlib.pyplot as plt
import numpy as np
from sklearn import datasets, linear_model

regr = linear_model.LinearRegression()

# Train the model using the training sets
regr.fit(x, y)

# Plot outputs
plt.scatter(x, y, color=’black’)
plt.plot(x, y, color=’blue’, linewidth=3)




Dep. Variable: y R-squared: 0.927
Model: OLS Adj. R-squared: 0.909
Method: Least Squares F-statistic: 51.16
Date: Mon, 08 Jan 2018 Prob (F-statistic): 0.00202
Time: 18:22:40 Log-Likelihood: -7.7047
No. Observations: 5 AIC: 17.41
Df Residuals: 4 BIC: 17.02
Df Model: 1
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
x1 1.2182 0.170 7.152 0.002 0.745 1.691
Omnibus: nan Durbin-Watson: 2.850
Prob(Omnibus): nan Jarque-Bera (JB): 1.307
Skew: 1.252 Prob(JB): 0.520
Kurtosis: 2.956 Cond. No. 1.00

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