Linear models: a classic example

import pandas as pd
import numpy as np
from sklearn.linear_model import LinearRegression
import matplotlib.pyplot as plt

dat = pd.read_csv("https://raw.githubusercontent.com/bcaffo/ds4bme_intro/master/data/swiss.csv")
dat.head()

	Region	Fertility	Agriculture	Examination	Education	Catholic	Infant.Mortality
0	Courtelary	80.2	17.0	15	12	9.96	22.2
1	Delemont	83.1	45.1	6	9	84.84	22.2
2	Franches-Mnt	92.5	39.7	5	5	93.40	20.2
3	Moutier	85.8	36.5	12	7	33.77	20.3
4	Neuveville	76.9	43.5	17	15	5.16	20.6

y = dat.Fertility
x = dat.drop(['Region', 'Fertility'], axis=1)
fit = LinearRegression().fit(x, y)
yhat = fit.predict(x)
[fit.intercept_, fit.coef_]

[66.9151816789687,
 array([-0.17211397, -0.25800824, -0.87094006,  0.10411533,  1.07704814])]

x2 = x
x2['Test'] = x2.Agriculture + x2.Examination
fit2 = LinearRegression().fit(x2, y)
yhat2 = fit2.predict(x2)

plt.plot(yhat, yhat2);

x3 = x2.drop(['Agriculture'], axis = 1)
fit3 = LinearRegression().fit(x3, y)
yhat3 = fit3.predict(x3)
plt.plot(yhat, yhat3);