簡單線性迴歸（Simple Linear Regression）下
阿新 • • 發佈：2019-01-01
1、簡單線性迴歸模型舉例：
汽車賣家做電視廣告數量與賣出的汽車數量：
如何訓練適合簡單線性迴歸模型的最佳迴歸線？
使sum of squares最小
計算
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
預測：假設有一週廣告數量為6，預測的汽車銷售量是多少？
x_given = 6
Y_hat = 5*6+10=40
import numpy as np def fitSLR(x,y): n = len(x) dinominator = 0#分子 numerator = 0#分母 for i in range(0,n): numerator += (x[i] - np.mean(x))*(y[i] - np.mean(y)) dinominator += (x[i] - np.mean(x))**2 print "numerator: ",numerator print "dinominaytor: ",dinominator 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
