First linear regression in Python

LinearRegression.py

__author__ = 'martinbodocky'

from numpy import *
import matplotlib.pyplot as plt
import csv


def loadDataSet(filename):
    """Load CSV comma formatted file without header,
    which contains features values and target value in last column
    """
    with open(filename) as csvfile:
        csvlines = csv.reader(csvfile, delimiter=',', quoting=csv.QUOTE_MINIMAL)
        dataMat = []
        targetMat = []
        for row in csvlines:
            numfeatures = len(row) - 1
            dataRow = []
            for num in row[:numfeatures]:
                dataRow.append(float(num))
            dataMat.append(dataRow)
            targetMat.append(float(row[-1]))
    return dataMat, targetMat


def normalEquation(xArr, yArr):
    """
    Functions applies normal equation for find optimal thetas
    """
    xMat = mat(xArr)
    yMat = mat(yArr).T
    xTx = xMat.T * xMat
    if linalg.det(xTx) == 0.0:
        print "This matrix is singular, cannot do inverse"
        return
    ws = xTx.I * (xMat.T * yMat)
    return ws


def showData(filename):
    x, y = loadDataSet(filename)
    xMat = mat(x)
    yMat = mat(y)

    #Basic scatter which displays data
    fig = plt.figure()
    ax = fig.add_subplot(111)
    ax.scatter(xMat[:, 0].flatten().A[0], yMat.T[:, 0].flatten().A[0])
    plt.show()


def showDataWithRegression(filename):
    x, y = loadDataSet(filename)
    xMat = mat(x)
    yMat = mat(y)

    # Linear regression by use Normal Equation
    theta = normalEquation(x, y)

    #compute target values
    fig = plt.figure()
    ax = fig.add_subplot(111)
    ax.scatter(xMat[:, 0].flatten().A[0], yMat.T[:, 0].flatten().A[0])

    xCopy = xMat.copy()
    xCopy.sort(0)
    yTarget = xCopy * theta
    ax.plot(xCopy[:, 0], yTarget)
    plt.show()

showData("Data/ex1data1.txt")
showDataWithRegression("Data/ex1data1.txt")