You want to plot the values, plt.scatter(x_values.values, y_values.values). It would also make sense to sort the data, to get a smooth line.
import numpy as np
import pandas as pd
from sklearn import linear_model
import matplotlib.pyplot as plt
#read data
dataframe = pd.read_fwf('data/brainbody.txt')
x_values = dataframe[['Brain']]
y_values = dataframe[['Body']]
#train model on data
body_reg = linear_model.LinearRegression()
body_reg.fit(x_values, y_values)
#visualize results
plt.scatter(x_values.values, y_values.values)
x = np.sort(x_values.values.flatten())
plt.plot(x, body_reg.predict(x[:,np.newaxis]))
plt.show()
