一元线性回归

1.根据数据画图；
2.根据所画图形进行分析，调整模型；
eg:
源代码1

clear all
clc
x=1:10;
y=[2650,1942,1493,1086,766,539,485,291,224,202];
z=zeros(size(y));
N=length(y);
for i =1:N
    z(i)=log(y(i));%调整
    plot(x(i),z(i),'ok');
    hold on
end

实验结果1

源代码2

clear all
clc
x=1:10;
y=[2650,1942,1493,1086,766,539,485,291,224,202];
z=zeros(size(y));
N=length(y);
for i =1:N
    z(i)=log(y(i));
end
[p,s]=polyfit(x,z,1)
y1=polyval(p,x);
hold on
plot(x,y1)

实验结果2

p =
   -0.2984    8.1671

s = 
  包含以下字段的 struct:

        R: [2×2 double]
       df: 8
    normr: 0.2316

p = polyfit(x,y,n); % 其中x,y表示需要拟合的坐标点，大小需要一样； n表示多项式拟合的次数。 %
返回值p表示多项式拟合的系数，系数从高到低排列

polyfit使用方法

多元线性回归

[b,bint,r,rint,stats]=regress(y,x，alpha)
alpha为显著性水平，缺省设定为0.05，b表示为输出输出量，bint为回归系数估计值和它们的置信区间，r为残差，rint为置信区间，stats适用于检验回归模型的统计量。
regress用法

例题：


实验分析及源代码：

clear all
clc
y=[90.9,97.4,113.5,125.7,122.8,133.3,149.3,144.2,166.4,195.0,229.8,228.7,206.1,257.9,324.1,386.6,423.0,401.9,474.9,424.5]
x1=[596.7,637.7,691.1,756,799,873.4,944,992.7,1077.6,1185.9,1326.4,1434.2,1549.2,1718,1918.3,2163.9,2417.8,2631.7,2954.7,3073]
x2=[0.7167,0.7277,0.7436,0.7676,0.7906,0.8254,0.8679,0.9145,0.9601,1,1.0575,1.1508,1.2579,1.3234,1.4005,1.5042,1.6342,1.7842,1.9514,2.0688]
y=[y'];
x=[ones(size(x1')),x1',x2'];
[b,bint,r,rint,stats]=regress(y,x)

实验结果

b =

  322.7250
    0.6185
 -859.4790


bint =

   1.0e+03 *

    0.2243    0.4211
    0.0005    0.0008
   -1.1215   -0.5975


r =

   15.1306
    5.7281
    2.4682
   -4.8421
  -14.5677
  -20.1710
  -11.3062
   -6.4733
    2.4119
   -1.6737
   -4.3468
    8.0729
    6.4006
   10.1010
   18.6900
   18.4250
    9.5311
  -14.9349
    2.0085
  -20.6521


rint =

   -8.8991   39.1602
  -20.0842   31.5404
  -23.8131   28.7495
  -30.9710   21.2868
  -39.7357   10.6002
  -44.1322    3.7901
  -37.1412   14.5288
  -32.9501   20.0034
  -24.3505   29.1743
  -28.4886   25.1412
  -30.1760   21.4823
  -18.6017   34.7476
  -16.4416   29.2428
  -15.3656   35.5677
   -6.2548   43.6348
   -4.6295   41.4795
  -13.7104   32.7727
  -39.1156    9.2458
  -22.1655   26.1825
  -38.3634   -2.9408


stats =

    0.9908  919.8529    0.0000  161.7073

与书本上答案相符

其他
polyfit使用方法
regress用法