Solution Example in R > mat [,1] [,2] [1,] 3 5.0 [2,] 4 5.5 [1,] 3 5.0 [2,] 4 5.5 [3,] 2 4.0 [4,] 6 7.0 [5,] 8 10.0 [6,] 2 5.0 [7,] 5 7.5 > m1.mat [1] 4.285714 > m2.mat [1] 6.285714 > v1.mat [1] 4.904762 > v2.mat [1] 4.154762 > cov.mat [,1] [,2] [1,] 4.904762 4.321429 [2,] 4.321429 4.154762 # 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

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= 0.57 0.31 0.29 0.29 0.28 0.54 R= 1 0.75 0.53 1 0.71 1 R23=0.71  relationship between yield Y and Z is positive and strongly correlated. Calculate manually & check solutions in R