;
PROC GLM; CLASS sex;
MODEL h w b=sex/MOUNI; MANOVA H=sex; RUN; 练习2.5
TITLE’多元方差分析：区组设计’； DATA ex2_5;
INPUT x y a b@@; CARDS;
175 155 1 1 175 110 2 1 170 110 3 1 170 90 4 1 ……… 105 75 1 10 113 75 2 10 113 75 3 10 113 75 4 10 ;
PROC GLM; CLASS a b;
MODEL x y=a b /NOUNI; MANOVA H=a b; RUN; 练习2.6
TITLE’多元方差分析：析因设计’; DATA ex2_6;
INPUT x1 x2 x3 a b @@; CARDS;
6.5 9.5 4.4 1 1 6.9 9.1 5.7 2 1 ... ... ...
6.8 8.5 3.4 1 2 7.6 9.2 1.9 2 2 ;
PROC GLM; CLASS a b;
MODEL x1 x2 x3=a b a*b; RUN;
第三章答案：
3-1答：设两样本Y1、Y2，样本含量分别为n1、n2，均数分别为Y1、Y2，标准差分别为s1、s2。
不妨设回归方程为：Y=a+bg
? 则当g=1时，Y1=a+bg=Y1；当g=0时，Y2=a=Y2。 故有b=Y2-Y1。 此
时
??????S
Y.s=
?2?(Y?Y)n?2=
?2?2(Y?Y)?(Y?Y?11?2?2)n?2n1(1?=
(n1?1)s1?(n2?1)s2n?222=
?(g?g)2=
n1n2 n则 tb=
n1(1?g)2?n1(0?g)2=
n1n1)2?n2(0?)2=
n1?n2n1?n2Y2?Y1b==t
22sb(n1?1)s1?(n2?1)s2n1n2/n?2n1?n2得证。
均数 2.4025 2.6850 3.0975 3-2答：TITLE’回归方程F检验与均数之方差分析’； DATA ex3_2;
INPUT y g g1 g2 @@; CARDS;
2.62 1 0 0 2.82 2 1 0 2.91 3 0 1 2.23 1 0 0 2.76 2 1 0 3.02 3 0 1 2.36 1 0 0 2.43 2 1 0 3.28 3 0 1 2.40 1 0 0 2.73 2 1 0 3.18 3 0 1 PROC REG;
MODEL y=g1 g2; RUN;
PROC ANOVA; CLASS g; MODEL y=g; RUN;
3-3答：TITLE’方差分析模型与线性回归模型’ DATA ex3_3; DO b=1 to 5; DO a=1 to 4; INPUT x @@; OUTPUT; END; END;
CARDS;
0.80 0.36 0.17 0.28 0.74 0.50 0.42 0.36 0.31 0.20 0.38 0.25 0.48 0.18 0.44 0.22 0.76 0.26 0.28 0.13 ;
PROC ANOVA; CLASS a b; MODEL x=a b; RUN;
PROC GLM; CLASS a b; MODEL x=a b; RUN;
3-4答：TITLE”筛选自变量的最优子集”； DATA ex3_4;
INPUT age weight runtime rstpulse maxpulse oxy; CARDS;
44 89.47 11.37 62 178 182 44.609
………
52 82.78 10.50 53 170 172 47.467
;
PROC REG RSQUARE MSE CP AIC ADJRSQ SELECT=2;
MODEL oxy=age weight runtime rstpulse runpulse maxpulse; run; 练习3.5
X1 X2 X3 X4 Y X1
1.000000 0.567021 0.209841 -0.043467 0.604392 X2
0.567021 1.000000 0.207706 0.741491 0.956619 X3
0.209841 0.207706 1.000000 0.100186 0.22781 X4 Y -0.043467 0.604392 0.741491 0.956619 0.100186 0.227810 1.000000 0.765506 0.765506 1.000000
以（2,2）为主元作消去变换，结果如下：
X1 X2 X3 X4 Y X1
0.678487 0.567021 0.092067 -0.463908 0.061969 X2
-0.567021 1.000000 -0.207706 -0.711491 -0.956619 X3
0.092067 0.207706 0.956858 -0.053826 0.029114 X4 Y -0.463908 0.061969 0.741491 0.956619 -0.053826 0.029114 0.450191 0.056182 0.056182 0.084880
以（4,4）为主元作消去变换，结果如下：
X1 X2 X3 X4 Y
X1 X2 X3 X4 Y 0.200144 1.331105 0.036601 -1.030469 0.119863 -1.331105 2.221279 -0.296361 -1.647059 -0.864084 0.036601 0.296361 0.950422 -0.119563 0.035831 1.030469 0.119863 -1.647059 0.864084 0.119563 0.035831 2.221279 0.124796 -0.124796 0.077869
以（1,1）为主元作消去变换，结果如下：
X1 X2 X3 X4 Y X1 X2
4.988925 -6.640783 -6.640783 11.060858 -0.182600 -0.053302 5.140932 -8.490180 -0.597987 -0.068100 X3 X4 Y
0.182600 5.140932 0.597987 0.053302 -8.490180 0.068100 6.943739 -0.068600 0.013944 0.068600 7.518850 0.741004 0.0139441 -0.741004 0.006192
以（2,2）为主元作消去变换，结果如下：
X1 X2 X3 X4 Y
练习3.6
X1
1.001893 -0.600386 -0.214602 0.043548 -0.638873 X2
0.600386 0.090409 0.004819 0.767588 0.006157 X3
0.214602 0.004819 6.943996 0.109514 1.001891 X4
0.043548 -0.767588 -0.109514 1.001891 -0.793277 Y
0.638873 0.006157 0.014272 0.793277 0.006611 因b0?y?b1x1?b2x2???bmxm，U??????bl?iiyxi，故：
?l^r^?yyyylyylyy???(yi?1ni?y)(yi?y)n^??^???(yi?1n?y)(b0?b1xi1???bmxim?y)lyyU
lyy??(yi?y)i?1?[(y?y)?b(xijnmij?xj)]???i?1j?1?b[?(y?y)(xjij?1j?1mm?ij?xj)]
?lYY?UlYY?U?bl?j?1mjyxilYY?U?U?R lYY得证。
练习3.7
TITLE”小学生的身高、年龄和体重的数据”; DATA ex3_7;
INPUT sex $ age height weight @@;
CARDS;
f 143 56.3 85.0 f 155 62.3 105.0 f 153 63.3 108.0 ... ... ...
m 164 61.5 140.0 m 167 62.0 107.5 m 151 59.3 87.0 ;
PROC REG OUTEST=est1 OUTSSCP=sscp1; BY sex;
EQ1:MODEL weight=height; EQ2:MODEL weight=height age; PROC PRINT DATA=sscp1; TITLE2”sscp类型的数据集”; PROC PRINT DATA=est1; TITLE2”est 类型的数据集”； RUN;
练习3.8
TITLE’逐步回归’;
OPTION LINESIZE=120; DATA ex3_8(TYPE=CORR); _TYPE_=”CORR”;
INPUT _name_$ x1 x2 x3 x4 x5 y; CARDS;
x1 1 . . . x2 -0.039603 1 .
. x3 -0.041057 0.965977 1 . x4 -0.034447 0.921631 0.938234 1 x5 0.047992 0.908298 0.915332 0.966865 y 0.037969 0.855474 0.883853 0.863441 ;
RUN;
PROC STEPWISE;
MODEL Y=x1 x2 x3 x4 x5/SLENTRY=0.15 SLSTAY=0.14 DETAILS; RUN;
练习3.9
TITLE’所有子集的回归’; DATA ex3_9;
INPUT x1 x2 x3 x4 x5 @@; CARDS;
289 101 109 107 73 3900 268 103 95 101 73 3200 ... ... ...
285 109 102 104 88 3800 276 106 193 103 74 3650
. . . .
1 0.850318 . . . . . 1