Matlab:回归分析，2

方法一：直接用多元二项式回归

1 %数据输入
2 x1 = [1000 600 1200 500 300 400 1300 1100 1300 300];
3 x2 = [5 7 6 6 8 7 5 4 3 9];
4 %多元二项式回归函数
5 y = [100 75 80 70 50 65 90 100 110 60];
6 X = [x1\' x2\'];
7 Y = y\';
8 rstool(X, Y, \'purequadratic\', 0.05);%使用纯二次模型

结果：

方法二：化为多元线性回归

1 %数据输入
2 x1 = [1000 600 1200 500 300 400 1300 1100 1300 300];
3 x2 = [5 7 6 6 8 7 5 4 3 9];
4 y = [100 75 80 70 50 65 90 100 110 60];
5 %多元线性回归
6 X = [ones(10, 1), x1\', x2\', (x1.^2)\' (x2.^2)\'];
7 Y = y\';
8 [b, bint, r, rint, states] = regress(Y, X, 0.05);
9 b, states

 1 %数据输入
 2 x = [20 25 30 35 40 45 50 55 60 65];
 3 y = [13.2 15.1 16.4 17.1 17.9 18.7 19.6 21.2 22.5 24.3];
 4 %X = [ones(10,1), x\'];
 5 %Y = y\';
 6 %[b, bint, r, rint, states] = regress(Y, X, 0.05);
 7 %rcoplot(r, rint)
 8 [P, S] = polyfit(x, y, 3);
 9 [Y, DELTA] = polyconf(P, 42, S, 0.05);
10 Y
11 [Y-DELTA, Y+DELTA]

结果：

Y =

18.3287

ans =

17.7891 18.8682

 1 x = [0 2 4 6 8 10 12 14 16 18 20];
 2 y = [0.6 2.0 4.4 7.5 11.8 17.1 23.3 31.2 39.6 49.7 61.7];
 3 %方法一：二次多项式回归
 4 [P, S] = polyfit(x, y, 2);
 5 P
 6 %方法二：转化为多元线性回归
 7 X = [ones(11, 1), x\', (x.^2)\'];
 8 Y = y\';
 9 b = regress(Y, X, 0.05);
10 b

结果：

P =

0.1403 0.1971 1.0105

b =

1.0105 0.1971 0.1403

1 function f = Q3fun(beta, x)
2 x1 = x(:,1);
3 x2 = x(:,2);
4 x3 = x(:,3);
5 f = (beta(1).*x2 - x3./beta(5)) ./ (1 + beta(2).*x1 + beta(3).*x2 + beta(4).*x3);

 1 %数据输入
 2 x1 = [470 285 470 470 470 100 100 470 100 100 100 285 285];
 3 x2 = [300 80 300 80 80 190 80 190 300 300 80 300 190];
 4 x3 = [10 10 120 120 10 10 65 65 54 120 120 10 120];
 5 y = [8.55 3.79 4.82 0.02 2.75 14.39 2.54 4.35 13.00 8.50 0.05 11.32 3.13];
 6 
 7 X = [x1\', x2\', x3\'];
 8 Y = y\';
 9 %参考值
10 beta0 = [1 0.05 0.02 0.1 2];
11 %非线性回归函数
12 [beta, r, J] = nlinfit(X, Y, \'Q3fun\', beta0);
13 beta
14 %预测及估计
15 nlintool(X, Y, \'Q3fun\', beta0, 0.05)

结果：

beta =

1.2526 0.0628 0.0400 0.1124 1.1914

置信区间

-0.746742266632702 3.25193260901551

-0.0376762702432533 0.163228825666061

-0.0311725427348701 0.111268700470180

-0.0608975612723978 0.285728748651990

-0.738086110268459 3.12082296226925