参考彭亮老师的视频教程:转载请注明出处及彭亮老师原创
视频教程: http://pan.baidu.com/s/1kVNe5EJ
1. 简单线性回归模型举例:
汽车卖家做电视广告数量与卖出的汽车数量:
1.1 如何练处适合简单线性回归模型的最佳回归线?
使sum of squares最小
1.1.2 计算
分子 = (1-2)(14-20)+(3-2)(24-20)+(2-2)(18-20)+(1-2)(17-20)+(3-2)(27-20) = 6 + 4 + 0 + 3 + 7 = 20
分母 = (1-2)^2 + (3-2)^2 + (2-2)^2 + (1-2)^2 + (3-2)^2 = 1 + 1 + 0 + 1 + 1 4
b1 = 20/4 =5
b0 = 20 - 5*2 = 20 - 10 = 10
1.2 预测:
假设有一周广告数量为6,预测的汽车销售量是多少?
x_given = 6
Y_hat = 5*6 + 10 = 40
1.3 Python实现:
import numpy as np
def fitSLR(x, y): n = len(x) dinominator = 0 numerator = 0 for i in range(0, n): numerator += (x[i] - np.mean(x))*(y[i] - np.mean(y)) dinominator += (x[i] - np.mean(x))**2 b1 = numerator/float(dinominator) b0 = np.mean(y)/float(np.mean(x)) return b0, b1
def predict(x, b0, b1): return b0 + x*b1
x = [1, 3, 2, 1, 3] y = [14, 24, 18, 17, 27]
b0, b1 = fitSLR(x, y)
print "intercept:", b0, " slope:", b1
x_test = 6
y_test = predict(6, b0, b1)
print "y_test:", y_test