浙大朱军生物统计作业 答案

下面对每个自变量用 t 检验：
t(α/2;n-p-1)=t(0.025;21)= 2.4138
̂
0.0187
1∗ = SE(1̂ )=0.0296=0.6081< t(0.025;21)
1
̂
2.073
2∗ = SE(2̂ )=0.270=7.6778> t(0.025;21)
2
̂
1.938
proc reg;
model lean= eye leg waist;
run;
2) Calculate the total sum of squares SSTO, residual sum squares SSE and adjusted
determinant coefficient for the model 2 ;
2)deduce(推断) the expectation and variance of random vector z ，what’s distribution
it follows ？
(2)
2()
4
2
E(z)=E* +=[
]=[
]=* +
− (−) −() −2
2
Var(z)=Var* +=Var(z) = E{[z－E(z)][z－E(z)]T}
meat on eye muscle meat, leg meat, waist meat. Suppose SSR =23.865，R 2=0.842，
̂0 (SE)= 0.857 (1.384),̂1 (SE)=0.0187(0.0296),̂2 (SE)=2.073(0.270)，̂3 (SE)=1.938
this random variable follows?
variable Y =
E(Y)=E(
;2
5
, = *
;2
();2
2;2
5
5
5
)=
Var(Y)=Var(
=
;2

=0;
1
25
)=Var( 5 )= 25 σ2 （X）=25=1；
5
This random variable Y follows standard normal distribution Y~N(0,1)
(0.513).
1) Please write out SAS statements for the step of procedure if the data set has been
established;
date lean;
input eye leg waist @@;
card;
……
……
……
；
Replicate（重复）
1) What’s the experimental design?
Experimental design is a body of knowledge and technique that enable an
investigator to conduct better experiments, analyze data efficiently, and make the
= 0.857 + 0.01871 + 2.0732 + 1.9383 +
原假设0 ：1 = 2 = 3 = 0
备择假设 H1：上式不成立
23.865
∗ = = 0.213 =112.042
F(0.05;p,n-p-1)=F(0.05;3,21)=3.07
−
2 − 4 2 − 4
4
4
2X
2X
=E,[* + － * +][* + － * +]-= E{*
+*
+ }
− + 2 − + 2
−X
−2 −X
−2
2 − 4
= E,*
+ [2 − 4 − + 2]− + 2
4( − 2)2 −2( − 2)2
4( − 2)2 −2( − 2)2
connection between the conclusions from the analysis and the original objective of the
investigation.
In this exercise the experimental design is Two-way Nested Designs(双因素巢式
= E[
]=[
]
−2( − 2)2
( − 2)2
−2( − 2)2
( − 2)2
T=
;

~N(0,1)
X = σ ∙ T + μ=5T+2
E(T)=0
:∞
( − 2)2 =E(5T + 2 − 2)2=E(5T)2=25E(T 2 )=25 ∫;∞ 2 ( 2 )
:∞
∴ ∗ >F(0.05;3,21) 否定原假设，接受备择假设。
方差分析表明，
F 检验达到极显著水平。因而瘦肉量 y 与眼肌面积x1 、腿肉量x2 、腰
肉量x3 存在回归关系。大约 82%的瘦肉量是由这三个产量构成因素决定的。
4) Conduct statistical test on the significance of each regression parameter, according

2 =
SSTO =
23.865
2
= 0.842 =28.343
SSTO=SSR+SSE
SSE=SSTO-SSR=28.343-23.865=4.478
MSE=SSE/(n-p-1)= 4.478/(25-3-1)=0.213
MSTO=SSTO/(n-1)= 28.343/24=1.181
that were carefully chosen to have different measurement values on the characteristic
of interest. The laboratories were required to perform three separate analyses of the
2 = 1 − /=1-0.213/1.181=0.820
3) Conduct statistical test on the linear relationship of lean meat on eye muscle meat,
leg meat, waist meat, and give out appropriate statistical inference（统计推断）;
Statistic
H0 :2 =0
1 : :2 ≠ 0
F ∗ = /()~F(2,6)
Null Hypothesis
Alternative Hypothesis
Statistic
2
H0 :
=0
2
1 : : ≠ 0
F ∗ = ()/~F(6,18)
2
(i) ~N(0，
)
变异来源
自由度
MS
L
M(L)
Error
3-1=2
3*(3-1)=6
MSL
MSM(L)
MSE
3*3*（3-1）=18
E(MS)随即
2
2 + 32 + 9
2 + 32
2
F 测验:
Null Hypothesis
Alternative Hypothesis
the statistic for testing significance of each effect. (不要求采用上表数据进行实际计
算)
2)
Y = + + (i) + ~N(, 2 + 2 +
i=1,2,3;
j=1,2,3;
k=1,2,3;
εijk ~N(0，2 ) ~N(0，2
(眼肌面积x1 )、leg meat (腿肉量2 )、waist meat (腰肉量3 ), a sample of 25 pigs
was sampled, and trait investigation was conduced. The model = 0 + 1 1 +
2 2 + 3 3 + was analyzed for the the multiple variable linear regression of lean
to the results of statistical test, is it necessary to modify(修改) the model? why ?
上面第二题 检验只是否定了所有自变量的回归参数均为零的假设 0 ：
1 = 2 = 3 = 0，但这并不能进一步判断认为每个自变量的回归参数均不为零。
设计)
2) Write out the factors and their levels of this trial;
factors
Material
Laboratory
Replicate
levels
1、2、3
1、2、3
1、2、3
3) Set up an ANOVA model for this trial, define each of variables in the model;
test, write out the matrix K and vector b.
0

0 1 0 0
K=*
Ư
2
3
3 ． The following data are a portion of the responses collected during an
inter-laboratory study. Each of the several laboratories was sent a number of materials
是第 j 项 material 的效应
i 表示第 i 个实验室
j 表示第 j 个实验材料
k 表示第 k 次重复
εijk 是残差效应，独立正态随机变量εijk ~N(0，2 )
4) If the model is a random model ( each effect is random effect in model), write out
=25 ∫;∞ 2
1
√2
;
2 /2
=25
4 × 25 −2 × 25 100 −50
∴Var(z)= *
+=*
+
−2 × 25
25
−50 25
4
100 −50
∴z~MVN(* + , *
+)
−2 −50 25
2. To study on the relationship between the lean meat (瘦肉量 y) with eye muscle area
test material.
Laboratory
Material
1
A
B
C
12.2
15.5
18.1
12.3
15.0
18.1
12.2
15.3
18.2
2
A
B
C
12.6
15.0
18.5
12.3
15.5
18.3
12.7
15.2
18.6
3
A
B
C
12.7
15.3
18.0
12.8
15.2
18.2
12.7
15.2
17.9
3∗ = SE(3̂ )=0.513=3.7778> t(0.025;21)
3
故1 不显著
故2 显著
故3 显著
所以此线性模型需要修改，修改为： = 0 + 2 2 + 3 3 +
5) If the equation of b1= 0.02, b3= 2.0 is required to be tested in one generalized linear
生物统计与试验设计——作业二
1. If a random variable X follows the normal distribution N(2, 25), let random
2
+,
−
1) what’s the expectation and variance of random variable Y，what’s the distribution
Factor M in Factor L
Factor L
1
1(1)
2(1)
3(1)
2
1(2)
2(2)
3(2)
3
1(3)
2(3)
3(3)
Y = + + (i) +
i=1,2,3;
j=1,2,3;
k=1,2,3;
μ是总体的均值
是第 i 项 laboratory 的效应