用matlab计算线性回归问题

看机器学习的时候遇到的第一个算法就是线性回归，高数中很详细的说明了线性回归的原理和最小2乘法的计算过程，很显然不适合手动计算，好在各种语言都有现成的函数使用，让我们愉快的做个调包侠吧

简单线性回归

r越接近1表示拟合效果越好

>> x=[0,1,2,3,4,5,6,7]

x =

     0     1     2     3     4     5     6     7

>> y=[27.0,26.8,26.5,26.3,26.1,25.7,25.3,24.8]

y =

  列 1 至 7

  27.000000000000000  26.800000000000001  26.500000000000000  26.300000000000001  26.100000000000001  25.699999999999999  25.300000000000001

  列 8

  24.800000000000001

>> [r,m,b]=regression(x,y)

r =

  -0.986307223369922


m =

  -0.303571428571428


b =

  27.124999999999996

>> plotregression(x,y)
>> 

多元线性回归

>> load carsmall
>> x1 = weight;
>> x2 = horsepower;
>> y = mpg;
>> x = [ones(size(x1)) x1 x2 x1.*x2];
>> b = regress(y,x)

b =

  60.710360805049135
  -0.010153547589001
  -0.188206440954574
   0.000038494827316

>> scatter3(x1,x2,y,'filled')
hold on
x1fit = min(x1):100:max(x1);
x2fit = min(x2):10:max(x2);
[x1fit,x2fit] = meshgrid(x1fit,x2fit);
yfit = b(1) + b(2)*x1fit + b(3)*x2fit + b(4)*x1fit.*x2fit;
mesh(x1fit,x2fit,yfit)
xlabel('weight')
ylabel('horsepower')
zlabel('mpg')
view(50,10)
hold off
>>