MLR.py

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# create arrays for the data points
X = []
Y = []

#read the csv file
csvReader = open('BloodPressure.csv')

#skips the header line
csvReader.readline()

for line in csvReader:
    y, x1, x2 = line.split(',')
    X.append([float(x1), float(x2), 1]) # add the bias term at the end
    Y.append(float(y))

# use numpy arrays so that we can use linear algebra later
X = np.array(X)
Y = np.array(Y)

# graph the data
fig = plt.figure(1)
ax = fig.add_subplot(111, projection='3d')
ax.scatter(X[:, 0], X[:, 1], Y)
ax.set_xlabel('Age')
ax.set_ylabel('Weight')
ax.set_zlabel('Blood Pressure')

# Use Linear Algebra to solve
a = np.linalg.solve(np.dot(X.T, X), np.dot(X.T, Y))
predictedY = np.dot(X, a)

# calculate the r-squared
SSres = Y - predictedY
SStot = Y - Y.mean()
rSquared = 1 - (SSres.dot(SSres) / SStot.dot(SStot))
print("the r-squared is: ", rSquared)
print("the coefficient (value of a) for age, weight, constant is: ", a)

# create a wiremesh for the plane that the predicted values will lie
xx, yy, zz = np.meshgrid(X[:, 0], X[:, 1], X[:, 2])
combinedArrays = np.vstack((xx.flatten(), yy.flatten(), zz.flatten())).T
Z = combinedArrays.dot(a)

# graph the original data, predicted data, and wiremesh plane
fig = plt.figure(2)
ax = fig.add_subplot(111, projection='3d')
ax.scatter(X[:, 0], X[:, 1], Y, color='r', label='Actual BP')
ax.scatter(X[:, 0], X[:, 1], predictedY, color='g', label='Predicted BP')
ax.plot_trisurf(combinedArrays[:, 0], combinedArrays[:, 1], Z, alpha=0.5)
ax.set_xlabel('Age')
ax.set_ylabel('Weight')
ax.set_zlabel('Blood Pressure')
ax.legend()
plt.show()