浙大朱军生物统计作业2答案

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0.0187 2.073 1.938
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 test, write out the matrix K and vector b. ������0 ������ 0 1 0 0 K=* + b=[ 1 ] ������ 0 0 0 1 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 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 test material. Laboratory 1 Material A B C A B C A B C 12.2 15.5 18.1 12.6 15.0 18.5 12.7 15.3 18.0 Replicate（重复） 12.3 15.0 18.1 12.3 15.5 18.3 12.8 15.2 18.2 12.2 15.3 18.2 12.7 15.2 18.6 12.7 15.2 17.9
2
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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 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 设计) 2) Write out the factors and their levels of this trial; factors levels Material 1、2、3 Laboratory 1、2、3 Replicate 1、2、3
������������������ 23.865
t(α/2;n-p-1)=t(0.025;21)= 2.4138
1 ∗ = SE(������ ������1 = =0.6081< t(0.025;21) ̂ ) 0.0296 1 2 ∗ = SE(������ ������2 = =7.6778> t(0.025;21) ̂ ) 0.270 2 3 ∗ = SE(������ ������3 = =3.7778> t(0.025;21) ̂ ) 0.513 3
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
2 ������������ = 1 − ������������������/������������������������=1-0.213/1.181=0.820 3) Conduct statistical test on the linear relationship of lean meat on eye muscle meat,
:∞ 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 (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 meat on eye muscle meat, leg meat, waist meat. Suppose SSR =23.865，R 2=0.842，
2 determinant coefficient for the model ������������ ;
������ 2 = ������������������������
������������������
SSTO =
������������������ 23.865 ������ 2
= 0.842 =28.343
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 this random variable follows? variable Y =
̂0 (SE)= 0.857 (1.384),������ ̂1 (SE)=0.0187(0.0296),������ ̂2 (SE)=2.073(0.270)，������ ̂3 (SE)=1.938 ������ (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; …… …… …… ； proc reg; model lean= eye leg waist; run; 2) Calculate the total sum of squares SSTO, residual sum squares SSE and adjusted
������;2 5
,������ = *
E(Y)=E(
������; 5
)=
������(������);2 5 5
=
2;2 5 ������
=0;
1 25
Var(Y)=Var(
������;2
)=Var( 5 )= 25 σ2 （X）=25=1；
This random variable Y follows standard normal distribution Y~N(0,1) 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} −������ 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 = E[ ] = [ ] −2(������ − 2)2 (������ − 2)2 −2������(������ − 2)2 ������(������ − 2)2 T=