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 >>
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