简单线性回归（下）

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 如何画出适合简单线性回归模型的最佳回归线？

使sum of squares最小

计算过程

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：

测试代码：

import numpy as npdef fitSLR(x,y):    n = len(x)    denominator = 0    numerator = 0    for i in range(0,n):        numerator += (x[i] - np.mean(x))*(y[i] - np.mean(y))        denominator += (x[i] - np.mean(x))**2    print("numerator: "+str(numerator))    print("denominator: "+str(denominator))    b1 = numerator/float(denominator)    b0 = np.mean(y) - b1*np.mean(x)    return b0,b1def predict(x,b0,b1):    return b0+x*b1x = [1,3,2,1,3]y = [14,24,18,17,27]b0,b1 = fitSLR(x,y)print("intercept: "+str(b0))print("slope: "+str(b1))x_test = 6y_test = predict(x_test,b0,b1)print("y_test: "+str(y_test))
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测试结果：

numerator: 20.0denominator: 4.0intercept: 10.0slope: 5.0y_test: 40.0