multivariate linear regression

multlin.py

def feature_normalize(X):
    '''
    Returns a normalized version of X where
    the mean value of each feature is 0 and the standard deviation
    is 1. This is often a good preprocessing step to do when
    working with learning algorithms.
    '''
    mean_r = []
    std_r = []

    X_norm = X

    n_c = X.shape[1]
    for i in range(n_c):
        m = mean(X[:, i])
        s = std(X[:, i])
        mean_r.append(m)
        std_r.append(s)
        X_norm[:, i] = (X_norm[:, i] - m) / s

    return X_norm, mean_r, std_r


def compute_cost(X, y, theta):
    '''
    Comput cost for linear regression
    '''
    #Number of training samples
    m = y.size

    predictions = X.dot(theta)

    sqErrors = (predictions - y)

    J = (1.0 / (2 * m)) * sqErrors.T.dot(sqErrors)

    return J


def gradient_descent(X, y, theta, alpha, num_iters):
    '''
    Performs gradient descent to learn theta
    by taking num_items gradient steps with learning
    rate alpha
    '''
    m = y.size
    J_history = zeros(shape=(num_iters, 1))

    for i in range(num_iters):

        predictions = X.dot(theta)

        theta_size = theta.size

        for it in range(theta_size):

            temp = X[:, it]
            temp.shape = (m, 1)

            errors_x1 = (predictions - y) * temp

            theta[it][0] = theta[it][0] - alpha * (1.0 / m) * errors_x1.sum()

        J_history[i, 0] = compute_cost(X, y, theta)

    return theta, J_history

In the feature_normalize(X): you have an error:
instead of : X_norm = X
you should do: X_norm = X.xopy()