1. Solution Example in R > mat [,1] [,2] [1,] 3 5.0 [2,] 4 5.5
[1,]
[2,]
[3,]
[4,]
[5,]
[6,]
[7,]
> m1.mat
[1]
> m2.mat
[1]
> v1.mat
[1]
> v2.mat
[1]
> cov.mat
[,1] [,2]
[1,]
[2,]
# Create matrix
> mat = matrix(c(3,4,2,6,8,2,5,5,5.5,4,7,10,5,7.5),7,2)
# sample mean for each variable
> m1.mat =mean(mat [,1])
> m2.mat =mean(mat [,2])
# sample variance for each variable
> v1.mat =var(mat [,1])
> v2.mat =var(mat [,2])
# covariance matrix
> cov.mat=var(mat)
Many mv methods are based on an underlying model

2. Calculate manually & check solutions in R
TASK 1
The yield of rice paddy have been measured in tonne/ha, which have randomly attributed to 3 lots prepared by one of three different fertilizers:
Yield X
Yield Y
Yield Z
1.3
1.9
4.3
4.2
4.4
2.6
2.9
3.4
3.1
3.2
3.5
2.1
3.3
2.4
2.7
4.5
1.6
2.3
2.8
(1) Calculate the arrays
for
(2) Interpret
Xbar=(2.56,2.93,3.17)
Sn=
0.54 R= 1
R23=0.71  relationship between yield Y and Z is positive and strongly correlated.
Calculate manually & check solutions in R