Linear regression with least square method

Beijing Institute of Technology | Ming-Jian Li

The following Python code is a companion code for the course on Artificial Intelligence and Simulation Science. It functions to fit a line using linear regression based on a given dataset and make predictions, with parameter optimization using the least square method.

​x
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import numpy as np
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import matplotlib.pyplot as plt
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# prepare data
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data = np.array([[3.2,31],[5.3,68],[6.1,62],[4.7,71],
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                 [5.9,87],[5.5,78],[5.2,79],[3.9,59],
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                 [4.8,75],[5.2,71],[4.5,55],[5.4,82],
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                 [4.4,62],[5.8,75],[5.6,81],[4.8,60],
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                 [4.4,82],[6.0,97],[4.5, 48],[3.8,56],
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                 [6.6,83],[6.5,118],[4.7,57],[4.1,51],
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                 [5.1,75],[5.9,74],[5.7,95],[6.3,95],
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                 [4.6,79],[5.0,83]])
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# get data
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x = data[:, 0]
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y = data[:, 1]
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# draw scatter
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plt.scatter(x, y)
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plt.show()
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# loss function
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def compute_cost(w, b, points):
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    total_cost = 0
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    M = len(points)
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    # average of square loss
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    for i in range(M):
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        x = points[i, 0]
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        y = points[i, 1]
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        total_cost += (y - w * x - b) ** 2
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    return total_cost / M
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# average function
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def average(data):
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    sum = 0
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    num = len(data)
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    for i in range(num):
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        sum += data[i]
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    return sum / num
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# fitting fucntion
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def fit(points):
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    M = len(points)
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    x_bar = average(points[:, 0])
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    sum_yx = 0
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    sum_x2 = 0
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    sum_delta = 0
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    for i in range(M):
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        x = points[i, 0]
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        y = points[i, 1]
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        sum_yx += y * (x - x_bar)
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        sum_x2 += x ** 2
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    # get w 
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    w = sum_yx / (sum_x2 - M * (x_bar ** 2))
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    for i in range(M):
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        x = points[i, 0]
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        y = points[i, 1]
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        sum_delta += (y - w * x)
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    b = sum_delta / M
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    return w, b
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# loss
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w, b = fit(data)
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print("w is: ", w)
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print("b is: ", b)
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cost = compute_cost(w, b, data)
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print("cost is: ", cost)
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# fit
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plt.scatter(x, y)
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# predict
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pred_y = w * x + b
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plt.plot(x, pred_y, c='r')
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plt.show()

The fitting results are as follows.