# STA 4210 solution for homework7

Pages: 13 (2089 words) Published: October 31, 2014

Homework
For
Quiz
7

Dingke
Yin

5.24

>
X=matrix(c(1,1,1,1,1,1,4,1,2,3,3,4),nrow=6,ncol=2)

>
Y=matrix(c(16,5,10,15,13,22),nrow=6,ncol=1)

>
solve(t(X)%*%X)%*%t(X)%*%Y

[,1]

[1,]
0.4390244

[2,]
4.6097561

>
Y-­‐X%*%solve(t(X)%*%X)%*%t(X)%*%Y

[,1]

[1,]
-­‐2.87804878

[2,]
-­‐0.04878049

[3,]

0.34146341

[4,]

0.73170732

[5,]
-­‐1.26829268

[6,]

3.12195122

>
J=matrix(1,6,6)

>
E=Y-­‐X%*%solve(t(X)%*%X)%*%t(X)%*%Y

>
t(E)%*%E

[,1]

[1,]
20.29268

>
t(Y)%*%(H-­‐1/6*J)%*%Y

[,1]

[1,]
145.2073

>
1/4*t(E)%*%E

[,1]

[1,]
5.073171

>
5.073171*solve(t(X)%*%X)

[,1]

[,2]

[1,]

6.805473
-­‐2.1035099

[2,]
-­‐2.103510

0.7424153

>
P=matrix(c(1,4),nrow=2,ncol=1)

>
t(P)%*%solve(t(X)%*%X)%*%t(X)%*%Y

[,1]

[1,]
18.87805

>
5.073171*(1+t(P)%*%solve(t(X)%*%X)%*%P)

[,1]

[1,]
6.929209

s^2{b1}=0.7424153

s{b0,b1}=
-­‐2.1035099

s{b0}=
2.608730

>
H=X%*%solve(t(X)%*%X)%*%t(X)

>
H

[,1]

[,2]

[,3]

[,4]

[,5]

[,6]

[1,]

0.36585366
-­‐0.1463415
0.02439024
0.1951220
0.1951220

0.36585366

[2,]
-­‐0.14634146

0.6585366
0.39024390
0.1219512
0.1219512
-­‐0.14634146

[3,]

0.02439024

0.3902439
0.26829268
0.1463415
0.1463415

0.02439024

[4,]

0.19512195

0.1219512
0.14634146
0.1707317
0.1707317

0.19512195

[5,]

0.19512195

0.1219512
0.14634146
0.1707317
0.1707317

0.19512195

[6,]

0.36585366
-­‐0.1463415
0.02439024