一、修改 regstats.m，增加关于自相关和异方差检验的 DW 和 GQ 统计量
见 regstats.m 文件
二、完成下列各题
第 1 题：
A=load('ex81.txt');
Y=A(:,1);
X=A(1:24,2:4);
X1=[ones(24,1) X];
[b,bint,r,rint,stats]= regress(Y,X1)
x=[1,5.1,20,7.2];
s=x*b
运行结果如下：
b =
17.8469
1.1031
0.3215
1.2889
bint =
13.6711 22.0228
0.4157 1.7906
0.2441 0.3989
0.6663 1.9116
r =
0.7359
1.9269
-0.0984
3.3089
-0.7142
1.2498
-2.1199
1.9845
-0.2501
1.3009
0.9063
-3.2382
-0.5629
-1.1931
-1.3116
-0.7518
0.1738
0.5478
-3.2463
1.1827
-0.8814
-1.4479
0.8148
1.6834
rint =
-2.6348 4.1066
-1.5933 5.4470
-3.5932 3.3964
0.0574 6.5603
-4.0225 2.5940
-2.1644 4.6640
-5.5005 1.2607
-1.2787 5.2477
-3.5163 3.0161
-1.8023 4.4040
-2.6592 4.4718
-6.3798 -0.0966
-3.6433 2.5175
-4.7105 2.3244
-4.6383 2.0151
-4.1890 2.6855
-3.0360 3.3837
-2.9079 4.0034
-6.2250 -0.2676
-2.1110 4.4764
-4.3799 2.6172
-4.8655 1.9696
-2.4650 4.0946
-1.7622 5.1289
stats =
0.9109 68.1192 0.0000 3.0722
s =
39.1837
所以回归方程为：y=17.8469+1.1031*x1+0.3215*x2+ 1.2889*x3;
当（x01,x02,x03)=(5.1.20.7.2)时，预测年工资为 s=39.1837 元。
系数置信区间分别为[13.6711,22.0228];[0.4157,1.7906];[0.2441,0.3989];
[0.6663,1.9116].
第 2 题：
编程如下：
x=0:2:20;
y=[0.6,2.0,4.4,7.5,11.8,17.1,23.3,31.2,39.6,49.7,61.7];
[p,S]=polyfit(x,y,2)
运行结果如下：
p =
0.1403 0.1971 1.0105
S =
R: [3x3 double]
df: 8
normr: 1.1097
所以二次多项式回归方程
为
第 3 题
编程如下：
步骤一：对将要拟合的非线性
模型，建立 m-文件 volum.m
如下：
function
yhat=volum(beta,x)
yhat=(beta(1).*x(:,2)-x(:,3)./beta(5))./
(1+beta(2).*x(:,1)+beta(3).*x(:,2)+beta(4).*x(:,3));
步骤二：输入数据：
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];
x=[470,285,470,470,470,100,100,470,100,100,100,285,285;300,80,300
,80,80,190,80,190,300,300,80,300,190;10,10,120,120,10,10,65,65,54
,120,120,10,120];
beta0=[1,0.05,0.02,0.1,2]';
步骤三：求回归系数：
[beta,r,J]=nlinfit(x',y','volum',beta0)
结果为：
beta =
1.2526
0.0628
0.0400
0.1124
1.1914
r =
0.1321
-0.1642
-0.0909
0.0310
0.1142
0.0498
-0.0262
0.3115
-0.0292
0.1096
0.0716
-0.1501
-0.3026
J =
6.8739 -90.6525 -57.8634 -1.9288 0.1614
3.4454 -48.5350 -13.6239 -1.7030 0.3034
5.3563 -41.2094 -26.3039 -10.5216 1.5095
1.6950 0.1091 0.0186 0.0278 1.7913
2.2967 -35.5653 -6.0537 -0.7567 0.2023
11.8669 -89.5648 -170.1730 -8.9565 0.4400
4.4973 -14.4261 -11.5409 -9.3769 2.5744
4.1831 -41.7891 -16.8935 -5.7794 1.0082
11.8285 -51.3718 -154.1151 -27.7408 1.5001
9.1514 -25.5946 -76.7838 -30.7135 2.5790
3.3373 0.0900 0.0720 0.1079 3.5269
9.3663 -102.0600 -107.4317 -3.5811 0.2200
4.7512 -24.4628 -16.3086 -10.3001 2.1141
所以回归模型为：
步骤四：预测并求置信区
间 C：
[Y,DELTA]=nlpredci('volum',x',beta,r,J)
C=[Y+DELTA Y-DELTA]
结果为：
Y =
8.4179
3.9542
4.9109
-0.0110
2.6358
14.3402
2.5662
4.0385
13.0292
8.3904
-0.0216
11.4701
3.4326
DELTA =
0.2805
0.2474
0.1766
0.1875
0.1578
0.4236
0.2425
0.1638
0.3426
0.3281
0.3699
0.3237
0.1749
