To convert MSR/MSRes, or the F statistic, to accomodate R^2, you mustremember that MSR=SSR/k, MSRes is SSRes/(n-k-1), F statistic is MSR/MSRes, SSR/SSRes can be written as SSR/SST, and R^2 is SSR/SSRes or 1-SSRes/SST. multiply both the numberator and demoniator with the ones they are usually divided by, or SSR(n-k-1)/SSResk, then seperate them like so: SSR/SSres * (n-k-1)/k, then convert SSR/SSRes to SSR/SSRes+SSR, which R^2=SSR/(SSRes+SSR) or 0.7=SSR/(SSRes+SSR), then both sides are multiplied by SSRes+SSR to get 0.7SSRes+0.7SSR=SSR, which SSR is then subtracted by 0.7 SSR to get 0.3SSR, which is then 0.7SSRes=0.3SSR, where SSR is divided by SSRes and 0.7 is divided by 0.3 to get SSR/SSres=0.7/0.3 or 2.3. The given units of n=20 and k=5 are used to make (20-5-1)/5 to get 14/5 or 2.4. 2.3*2.4 obtains 6.44, which the result in pf then subtracts 1 to obtain the answer
(0.7-1)*((20-5-1)/5)## [1] -0.84pf(5, 14, 6.44)## [1] 0.97564281-0.9756428## [1] 0.0243572This is an R programming for developing a matrix seen in HW2, but for wine quality than engine efficiency. This will take the variable pH(x2), total SO2 content (x3), color density (x4), polymeric pigment color (x6), anthocyanin color, (x7), total anthocyanins (x8) and density of ionization (x9) After developing X, W is created through the unit length scaling equations, which involve using xij for each of the 32 by 7 x answers for the matrix and -xi that is the mean of those x column answers (e.g. put the results of each x1 answer in the equation, while the mean is the mean of x1). I will perform manual unit length scaling and then do the correlation check afterwards This is (ULS) of X2
library(MPV)## Loading required package: lattice## Loading required package: KernSmooth## KernSmooth 2.23 loaded
## Copyright M. P. Wand 1997-2009## Loading required package: randomForest## Warning: package 'randomForest' was built under R version 4.1.3## randomForest 4.7-1.1## Type rfNews() to see new features/changes/bug fixes.table.b19## y x1 x2 x3 x4 x5 x6 x7 x8 x9 x10
## 1 19.2 0 3.85 66 9.35 5.65 2.40 3.25 0.33 19 0.065
## 2 18.3 0 3.73 79 11.15 6.95 3.15 3.80 0.36 21 0.076
## 3 17.1 0 3.88 73 9.40 5.75 2.10 3.65 0.40 18 0.073
## 4 17.3 0 3.86 99 12.85 7.70 3.90 3.80 0.35 22 0.076
## 5 16.8 0 3.98 75 8.55 5.05 2.05 3.00 0.49 12 0.060
## 6 16.5 0 3.85 61 10.30 6.20 2.50 3.70 0.38 20 0.074
## 7 15.8 0 3.93 66 4.90 2.75 1.20 1.55 0.29 11 0.031
## 8 15.2 0 3.66 86 6.40 4.00 1.50 2.50 0.27 19 0.050
## 9 15.2 0 3.91 78 5.80 3.30 1.40 1.90 0.40 9 0.038
## 10 14.0 0 3.47 178 3.60 2.25 0.75 1.50 0.37 8 0.030
## 11 14.0 0 3.91 81 3.90 2.15 1.00 1.15 0.32 7 0.023
## 12 13.8 0 3.75 108 5.80 3.20 1.60 1.60 0.38 8 0.032
## 13 13.6 0 3.90 92 5.40 2.85 1.55 1.30 0.44 6 0.026
## 14 12.8 0 3.92 96 5.00 2.70 1.40 1.30 0.35 7 0.026
## 15 18.5 1 3.87 89 9.15 5.60 1.95 3.65 0.46 16 0.073
## 16 17.3 1 3.97 59 10.25 6.10 2.40 3.70 0.40 19 0.074
## 17 16.3 1 3.76 22 8.20 5.00 1.85 3.15 0.25 25 0.063
## 18 16.3 1 3.76 77 8.35 5.05 1.90 3.15 0.37 17 0.063
## 19 16.0 1 3.98 58 10.15 6.00 2.60 3.40 0.38 18 0.068
## 20 16.0 1 3.88 85 6.85 4.10 1.50 2.60 0.33 16 0.052
## 21 15.7 1 3.75 120 8.80 5.50 1.85 3.65 0.39 19 0.073
## 22 15.5 1 3.98 94 5.45 3.05 1.50 1.55 0.41 8 0.031
## 23 15.3 1 3.69 122 8.00 5.05 1.90 3.15 0.27 23 0.063
## 24 15.3 1 3.77 144 5.60 3.35 1.10 2.25 0.36 12 0.045
## 25 14.8 1 3.74 10 7.90 4.75 1.95 2.80 0.25 23 0.056
## 26 14.3 1 3.76 100 5.55 3.25 1.15 2.10 0.34 12 0.042
## 27 14.3 1 3.91 73 4.65 2.70 0.95 1.75 0.36 10 0.035
## 28 14.2 1 3.60 301 4.25 2.40 1.25 1.15 0.42 6 0.023
## 29 14.0 1 3.76 104 8.70 5.10 2.25 2.85 0.34 17 0.057
## 30 13.8 1 3.90 67 7.40 4.40 1.60 2.80 0.45 13 0.056
## 31 12.5 1 3.80 89 5.35 3.15 1.20 1.95 0.32 12 0.039
## 32 11.5 1 3.65 192 6.35 3.90 1.25 2.65 0.63 8 0.053attach(table.b19)
X <- cbind(1, x2, x3, x4, x6, x7, x8, x9)
X## x2 x3 x4 x6 x7 x8 x9
## [1,] 1 3.85 66 9.35 2.40 3.25 0.33 19
## [2,] 1 3.73 79 11.15 3.15 3.80 0.36 21
## [3,] 1 3.88 73 9.40 2.10 3.65 0.40 18
## [4,] 1 3.86 99 12.85 3.90 3.80 0.35 22
## [5,] 1 3.98 75 8.55 2.05 3.00 0.49 12
## [6,] 1 3.85 61 10.30 2.50 3.70 0.38 20
## [7,] 1 3.93 66 4.90 1.20 1.55 0.29 11
## [8,] 1 3.66 86 6.40 1.50 2.50 0.27 19
## [9,] 1 3.91 78 5.80 1.40 1.90 0.40 9
## [10,] 1 3.47 178 3.60 0.75 1.50 0.37 8
## [11,] 1 3.91 81 3.90 1.00 1.15 0.32 7
## [12,] 1 3.75 108 5.80 1.60 1.60 0.38 8
## [13,] 1 3.90 92 5.40 1.55 1.30 0.44 6
## [14,] 1 3.92 96 5.00 1.40 1.30 0.35 7
## [15,] 1 3.87 89 9.15 1.95 3.65 0.46 16
## [16,] 1 3.97 59 10.25 2.40 3.70 0.40 19
## [17,] 1 3.76 22 8.20 1.85 3.15 0.25 25
## [18,] 1 3.76 77 8.35 1.90 3.15 0.37 17
## [19,] 1 3.98 58 10.15 2.60 3.40 0.38 18
## [20,] 1 3.88 85 6.85 1.50 2.60 0.33 16
## [21,] 1 3.75 120 8.80 1.85 3.65 0.39 19
## [22,] 1 3.98 94 5.45 1.50 1.55 0.41 8
## [23,] 1 3.69 122 8.00 1.90 3.15 0.27 23
## [24,] 1 3.77 144 5.60 1.10 2.25 0.36 12
## [25,] 1 3.74 10 7.90 1.95 2.80 0.25 23
## [26,] 1 3.76 100 5.55 1.15 2.10 0.34 12
## [27,] 1 3.91 73 4.65 0.95 1.75 0.36 10
## [28,] 1 3.60 301 4.25 1.25 1.15 0.42 6
## [29,] 1 3.76 104 8.70 2.25 2.85 0.34 17
## [30,] 1 3.90 67 7.40 1.60 2.80 0.45 13
## [31,] 1 3.80 89 5.35 1.20 1.95 0.32 12
## [32,] 1 3.65 192 6.35 1.25 2.65 0.63 8(X[1,2]-mean(X[,2]))/sqrt((X[1,2]-mean(X[,2]))^2)## x2
## 1(X[2,2]-mean(X[,2]))/sqrt((X[2,2]-mean(X[,2]))^2)## x2
## -1(X[3,2]-mean(X[,2]))/sqrt((X[3,2]-mean(X[,2]))^2)## x2
## 1(X[4,2]-mean(X[,2]))/sqrt((X[4,2]-mean(X[,2]))^2)## x2
## 1(X[5,2]-mean(X[,2]))/sqrt((X[5,2]-mean(X[,2]))^2)## x2
## 1(X[6,2]-mean(X[,2]))/sqrt((X[6,2]-mean(X[,2]))^2)## x2
## 1(X[7,2]-mean(X[,2]))/sqrt((X[7,2]-mean(X[,2]))^2)## x2
## 1(X[8,2]-mean(X[,2]))/sqrt((X[8,2]-mean(X[,2]))^2)## x2
## -1(X[9,2]-mean(X[,2]))/sqrt((X[9,2]-mean(X[,2]))^2)## x2
## 1(X[10,2]-mean(X[,2]))/sqrt((X[10,2]-mean(X[,2]))^2)## x2
## -1(X[11,2]-mean(X[,2]))/sqrt((X[11,2]-mean(X[,2]))^2)## x2
## 1(X[12,2]-mean(X[,2]))/sqrt((X[12,2]-mean(X[,2]))^2)## x2
## -1(X[13,2]-mean(X[,2]))/sqrt((X[13,2]-mean(X[,2]))^2)## x2
## 1(X[14,2]-mean(X[,2]))/sqrt((X[14,2]-mean(X[,2]))^2)## x2
## 1(X[15,2]-mean(X[,2]))/sqrt((X[15,2]-mean(X[,2]))^2)## x2
## 1(X[16,2]-mean(X[,2]))/sqrt((X[16,2]-mean(X[,2]))^2)## x2
## 1(X[17,2]-mean(X[,2]))/sqrt((X[17,2]-mean(X[,2]))^2)## x2
## -1(X[18,2]-mean(X[,2]))/sqrt((X[18,2]-mean(X[,2]))^2)## x2
## -1(X[19,2]-mean(X[,2]))/sqrt((X[19,2]-mean(X[,2]))^2)## x2
## 1(X[20,2]-mean(X[,2]))/sqrt((X[20,2]-mean(X[,2]))^2)## x2
## 1(X[21,2]-mean(X[,2]))/sqrt((X[21,2]-mean(X[,2]))^2)## x2
## -1(X[22,2]-mean(X[,2]))/sqrt((X[22,2]-mean(X[,2]))^2)## x2
## 1(X[23,2]-mean(X[,2]))/sqrt((X[23,2]-mean(X[,2]))^2)## x2
## -1(X[24,2]-mean(X[,2]))/sqrt((X[24,2]-mean(X[,2]))^2)## x2
## -1(X[25,2]-mean(X[,2]))/sqrt((X[25,2]-mean(X[,2]))^2)## x2
## -1(X[26,2]-mean(X[,2]))/sqrt((X[26,2]-mean(X[,2]))^2)## x2
## -1(X[27,2]-mean(X[,2]))/sqrt((X[27,2]-mean(X[,2]))^2)## x2
## 1(X[28,2]-mean(X[,2]))/sqrt((X[28,2]-mean(X[,2]))^2)## x2
## -1(X[29,2]-mean(X[,2]))/sqrt((X[29,2]-mean(X[,2]))^2)## x2
## -1(X[30,2]-mean(X[,2]))/sqrt((X[30,2]-mean(X[,2]))^2)## x2
## 1(X[31,2]-mean(X[,2]))/sqrt((X[31,2]-mean(X[,2]))^2)## x2
## -1(X[32,2]-mean(X[,2]))/sqrt((X[32,2]-mean(X[,2]))^2)## x2
## -1This is for X3:
(X[1,3]-mean(X[,3]))/sqrt((X[1,3]-mean(X[,3]))^2)## x3
## -1(X[2,3]-mean(X[,3]))/sqrt((X[2,3]-mean(X[,3]))^2)## x3
## -1(X[3,3]-mean(X[,3]))/sqrt((X[3,3]-mean(X[,3]))^2)## x3
## -1(X[4,3]-mean(X[,3]))/sqrt((X[4,3]-mean(X[,3]))^2)## x3
## 1(X[5,3]-mean(X[,3]))/sqrt((X[5,3]-mean(X[,3]))^2)## x3
## -1(X[6,3]-mean(X[,3]))/sqrt((X[6,3]-mean(X[,3]))^2)## x3
## -1(X[7,3]-mean(X[,3]))/sqrt((X[7,3]-mean(X[,3]))^2)## x3
## -1(X[8,3]-mean(X[,3]))/sqrt((X[8,3]-mean(X[,3]))^2)## x3
## -1(X[9,3]-mean(X[,3]))/sqrt((X[9,3]-mean(X[,3]))^2)## x3
## -1(X[10,3]-mean(X[,3]))/sqrt((X[10,3]-mean(X[,3]))^2)## x3
## 1(X[11,3]-mean(X[,3]))/sqrt((X[11,3]-mean(X[,3]))^2)## x3
## -1(X[12,3]-mean(X[,3]))/sqrt((X[12,3]-mean(X[,3]))^2)## x3
## 1(X[13,3]-mean(X[,3]))/sqrt((X[13,3]-mean(X[,3]))^2)## x3
## -1(X[14,3]-mean(X[,3]))/sqrt((X[14,3]-mean(X[,3]))^2)## x3
## 1(X[15,3]-mean(X[,3]))/sqrt((X[15,3]-mean(X[,3]))^2)## x3
## -1(X[16,3]-mean(X[,3]))/sqrt((X[16,3]-mean(X[,3]))^2)## x3
## -1(X[17,3]-mean(X[,3]))/sqrt((X[17,3]-mean(X[,3]))^2)## x3
## -1(X[18,3]-mean(X[,3]))/sqrt((X[18,3]-mean(X[,3]))^2)## x3
## -1(X[19,3]-mean(X[,3]))/sqrt((X[19,3]-mean(X[,3]))^2)## x3
## -1(X[20,3]-mean(X[,3]))/sqrt((X[20,3]-mean(X[,3]))^2)## x3
## -1(X[21,3]-mean(X[,3]))/sqrt((X[21,3]-mean(X[,3]))^2)## x3
## 1(X[22,3]-mean(X[,3]))/sqrt((X[22,3]-mean(X[,3]))^2)## x3
## -1(X[23,3]-mean(X[,3]))/sqrt((X[23,3]-mean(X[,3]))^2)## x3
## 1(X[24,3]-mean(X[,3]))/sqrt((X[24,3]-mean(X[,3]))^2)## x3
## 1(X[25,3]-mean(X[,3]))/sqrt((X[25,3]-mean(X[,3]))^2)## x3
## -1(X[26,3]-mean(X[,3]))/sqrt((X[26,3]-mean(X[,3]))^2)## x3
## 1(X[27,3]-mean(X[,3]))/sqrt((X[27,3]-mean(X[,3]))^2)## x3
## -1(X[28,3]-mean(X[,3]))/sqrt((X[28,3]-mean(X[,3]))^2)## x3
## 1(X[29,3]-mean(X[,3]))/sqrt((X[29,3]-mean(X[,3]))^2)## x3
## 1(X[30,3]-mean(X[,3]))/sqrt((X[30,3]-mean(X[,3]))^2)## x3
## -1(X[31,3]-mean(X[,3]))/sqrt((X[31,3]-mean(X[,3]))^2)## x3
## -1(X[32,3]-mean(X[,3]))/sqrt((X[32,3]-mean(X[,3]))^2)## x3
## 1This is X4
(X[1,4]-mean(X[,4]))/sqrt((X[1,4]-mean(X[,4]))^2)## x4
## 1(X[2,4]-mean(X[,4]))/sqrt((X[2,4]-mean(X[,4]))^2)## x4
## 1(X[3,4]-mean(X[,4]))/sqrt((X[3,4]-mean(X[,4]))^2)## x4
## 1(X[4,4]-mean(X[,4]))/sqrt((X[4,4]-mean(X[,4]))^2)## x4
## 1(X[5,4]-mean(X[,4]))/sqrt((X[5,4]-mean(X[,4]))^2)## x4
## 1(X[6,4]-mean(X[,4]))/sqrt((X[6,4]-mean(X[,4]))^2)## x4
## 1(X[7,4]-mean(X[,4]))/sqrt((X[7,4]-mean(X[,4]))^2)## x4
## -1(X[8,4]-mean(X[,4]))/sqrt((X[8,4]-mean(X[,4]))^2)## x4
## -1(X[9,4]-mean(X[,4]))/sqrt((X[9,4]-mean(X[,4]))^2)## x4
## -1(X[10,4]-mean(X[,4]))/sqrt((X[10,4]-mean(X[,4]))^2)## x4
## -1(X[11,4]-mean(X[,4]))/sqrt((X[11,4]-mean(X[,4]))^2)## x4
## -1(X[12,4]-mean(X[,4]))/sqrt((X[12,4]-mean(X[,4]))^2)## x4
## -1(X[13,4]-mean(X[,4]))/sqrt((X[13,4]-mean(X[,4]))^2)## x4
## -1(X[14,4]-mean(X[,4]))/sqrt((X[14,4]-mean(X[,4]))^2)## x4
## -1(X[15,4]-mean(X[,4]))/sqrt((X[15,4]-mean(X[,4]))^2)## x4
## 1(X[16,4]-mean(X[,4]))/sqrt((X[16,4]-mean(X[,4]))^2)## x4
## 1(X[17,4]-mean(X[,4]))/sqrt((X[17,4]-mean(X[,4]))^2)## x4
## 1(X[18,4]-mean(X[,4]))/sqrt((X[18,4]-mean(X[,4]))^2)## x4
## 1(X[19,4]-mean(X[,4]))/sqrt((X[19,4]-mean(X[,4]))^2)## x4
## 1(X[20,4]-mean(X[,4]))/sqrt((X[20,4]-mean(X[,4]))^2)## x4
## -1(X[21,4]-mean(X[,4]))/sqrt((X[21,4]-mean(X[,4]))^2)## x4
## 1(X[22,4]-mean(X[,4]))/sqrt((X[22,4]-mean(X[,4]))^2)## x4
## -1(X[23,4]-mean(X[,4]))/sqrt((X[23,4]-mean(X[,4]))^2)## x4
## 1(X[24,4]-mean(X[,4]))/sqrt((X[24,4]-mean(X[,4]))^2)## x4
## -1(X[25,4]-mean(X[,4]))/sqrt((X[25,4]-mean(X[,4]))^2)## x4
## 1(X[26,4]-mean(X[,4]))/sqrt((X[26,4]-mean(X[,4]))^2)## x4
## -1(X[27,4]-mean(X[,4]))/sqrt((X[27,4]-mean(X[,4]))^2)## x4
## -1(X[28,4]-mean(X[,4]))/sqrt((X[28,4]-mean(X[,4]))^2)## x4
## -1(X[29,4]-mean(X[,4]))/sqrt((X[29,4]-mean(X[,4]))^2)## x4
## 1(X[30,4]-mean(X[,4]))/sqrt((X[30,4]-mean(X[,4]))^2)## x4
## 1(X[31,4]-mean(X[,4]))/sqrt((X[31,4]-mean(X[,4]))^2)## x4
## -1(X[32,4]-mean(X[,4]))/sqrt((X[32,4]-mean(X[,4]))^2)## x4
## -1This is X6
(X[1,6]-mean(X[,6]))/sqrt((X[1,6]-mean(X[,6]))^2)## x7
## 1(X[2,6]-mean(X[,6]))/sqrt((X[2,6]-mean(X[,6]))^2)## x7
## 1(X[3,6]-mean(X[,6]))/sqrt((X[3,6]-mean(X[,6]))^2)## x7
## 1(X[4,6]-mean(X[,6]))/sqrt((X[4,6]-mean(X[,6]))^2)## x7
## 1(X[5,6]-mean(X[,6]))/sqrt((X[5,6]-mean(X[,6]))^2)## x7
## 1(X[6,6]-mean(X[,6]))/sqrt((X[6,6]-mean(X[,6]))^2)## x7
## 1(X[7,6]-mean(X[,6]))/sqrt((X[7,6]-mean(X[,6]))^2)## x7
## -1(X[8,6]-mean(X[,6]))/sqrt((X[8,6]-mean(X[,6]))^2)## x7
## -1(X[9,6]-mean(X[,6]))/sqrt((X[9,6]-mean(X[,6]))^2)## x7
## -1(X[10,6]-mean(X[,6]))/sqrt((X[10,6]-mean(X[,6]))^2)## x7
## -1(X[11,6]-mean(X[,6]))/sqrt((X[11,6]-mean(X[,6]))^2)## x7
## -1(X[12,6]-mean(X[,6]))/sqrt((X[12,6]-mean(X[,6]))^2)## x7
## -1(X[13,6]-mean(X[,6]))/sqrt((X[13,6]-mean(X[,6]))^2)## x7
## -1(X[14,6]-mean(X[,6]))/sqrt((X[14,6]-mean(X[,6]))^2)## x7
## -1(X[15,6]-mean(X[,6]))/sqrt((X[15,6]-mean(X[,6]))^2)## x7
## 1(X[16,6]-mean(X[,6]))/sqrt((X[16,6]-mean(X[,6]))^2)## x7
## 1(X[17,6]-mean(X[,6]))/sqrt((X[17,6]-mean(X[,6]))^2)## x7
## 1(X[18,6]-mean(X[,6]))/sqrt((X[18,6]-mean(X[,6]))^2)## x7
## 1(X[19,6]-mean(X[,6]))/sqrt((X[19,6]-mean(X[,6]))^2)## x7
## 1(X[20,6]-mean(X[,6]))/sqrt((X[20,6]-mean(X[,6]))^2)## x7
## 1(X[21,6]-mean(X[,6]))/sqrt((X[21,6]-mean(X[,6]))^2)## x7
## 1(X[22,6]-mean(X[,6]))/sqrt((X[22,6]-mean(X[,6]))^2)## x7
## -1(X[23,6]-mean(X[,6]))/sqrt((X[23,6]-mean(X[,6]))^2)## x7
## 1(X[24,6]-mean(X[,6]))/sqrt((X[24,6]-mean(X[,6]))^2)## x7
## -1(X[25,6]-mean(X[,6]))/sqrt((X[25,6]-mean(X[,6]))^2)## x7
## 1(X[26,6]-mean(X[,6]))/sqrt((X[26,6]-mean(X[,6]))^2)## x7
## -1(X[27,6]-mean(X[,6]))/sqrt((X[27,6]-mean(X[,6]))^2)## x7
## -1(X[28,6]-mean(X[,6]))/sqrt((X[28,6]-mean(X[,6]))^2)## x7
## -1(X[29,6]-mean(X[,6]))/sqrt((X[29,6]-mean(X[,6]))^2)## x7
## 1(X[30,6]-mean(X[,6]))/sqrt((X[30,6]-mean(X[,6]))^2)## x7
## 1(X[31,6]-mean(X[,6]))/sqrt((X[31,6]-mean(X[,6]))^2)## x7
## -1(X[32,6]-mean(X[,6]))/sqrt((X[32,6]-mean(X[,6]))^2)## x7
## 1This is X7
(X[1,7]-mean(X[,7]))/sqrt((X[1,7]-mean(X[,7]))^2)## x8
## -1(X[2,7]-mean(X[,7]))/sqrt((X[2,7]-mean(X[,7]))^2)## x8
## -1(X[3,7]-mean(X[,7]))/sqrt((X[3,7]-mean(X[,7]))^2)## x8
## 1(X[4,7]-mean(X[,7]))/sqrt((X[4,7]-mean(X[,7]))^2)## x8
## -1(X[5,7]-mean(X[,7]))/sqrt((X[5,7]-mean(X[,7]))^2)## x8
## 1(X[6,7]-mean(X[,7]))/sqrt((X[6,7]-mean(X[,7]))^2)## x8
## 1(X[7,7]-mean(X[,7]))/sqrt((X[7,7]-mean(X[,7]))^2)## x8
## -1(X[8,7]-mean(X[,7]))/sqrt((X[8,7]-mean(X[,7]))^2)## x8
## -1(X[9,7]-mean(X[,7]))/sqrt((X[9,7]-mean(X[,7]))^2)## x8
## 1(X[10,7]-mean(X[,7]))/sqrt((X[10,7]-mean(X[,7]))^2)## x8
## -1(X[11,7]-mean(X[,7]))/sqrt((X[11,7]-mean(X[,7]))^2)## x8
## -1(X[12,7]-mean(X[,7]))/sqrt((X[12,7]-mean(X[,7]))^2)## x8
## 1(X[13,7]-mean(X[,7]))/sqrt((X[13,7]-mean(X[,7]))^2)## x8
## 1(X[14,7]-mean(X[,7]))/sqrt((X[14,7]-mean(X[,7]))^2)## x8
## -1(X[15,7]-mean(X[,7]))/sqrt((X[15,7]-mean(X[,7]))^2)## x8
## 1(X[16,7]-mean(X[,7]))/sqrt((X[16,7]-mean(X[,7]))^2)## x8
## 1(X[17,7]-mean(X[,7]))/sqrt((X[17,7]-mean(X[,7]))^2)## x8
## -1(X[18,7]-mean(X[,7]))/sqrt((X[18,7]-mean(X[,7]))^2)## x8
## -1(X[19,7]-mean(X[,7]))/sqrt((X[19,7]-mean(X[,7]))^2)## x8
## 1(X[20,7]-mean(X[,7]))/sqrt((X[20,7]-mean(X[,7]))^2)## x8
## -1(X[21,7]-mean(X[,7]))/sqrt((X[21,7]-mean(X[,7]))^2)## x8
## 1(X[22,7]-mean(X[,7]))/sqrt((X[22,7]-mean(X[,7]))^2)## x8
## 1(X[23,7]-mean(X[,7]))/sqrt((X[23,7]-mean(X[,7]))^2)## x8
## -1(X[24,7]-mean(X[,7]))/sqrt((X[24,7]-mean(X[,7]))^2)## x8
## -1(X[25,7]-mean(X[,7]))/sqrt((X[25,7]-mean(X[,7]))^2)## x8
## -1(X[26,7]-mean(X[,7]))/sqrt((X[26,7]-mean(X[,7]))^2)## x8
## -1(X[27,7]-mean(X[,7]))/sqrt((X[27,7]-mean(X[,7]))^2)## x8
## -1(X[28,7]-mean(X[,7]))/sqrt((X[28,7]-mean(X[,7]))^2)## x8
## 1(X[29,7]-mean(X[,7]))/sqrt((X[29,7]-mean(X[,7]))^2)## x8
## -1(X[30,7]-mean(X[,7]))/sqrt((X[30,7]-mean(X[,7]))^2)## x8
## 1(X[31,7]-mean(X[,7]))/sqrt((X[31,7]-mean(X[,7]))^2)## x8
## -1(X[32,7]-mean(X[,7]))/sqrt((X[32,7]-mean(X[,7]))^2)## x8
## 1This is X8
(X[1,8]-mean(X[,8]))/sqrt((X[1,8]-mean(X[,8]))^2)## x9
## 1(X[2,8]-mean(X[,8]))/sqrt((X[2,8]-mean(X[,8]))^2)## x9
## 1(X[3,8]-mean(X[,8]))/sqrt((X[3,8]-mean(X[,8]))^2)## x9
## 1(X[4,8]-mean(X[,8]))/sqrt((X[4,8]-mean(X[,8]))^2)## x9
## 1(X[5,8]-mean(X[,8]))/sqrt((X[5,8]-mean(X[,8]))^2)## x9
## -1(X[6,8]-mean(X[,8]))/sqrt((X[6,8]-mean(X[,8]))^2)## x9
## 1(X[7,8]-mean(X[,8]))/sqrt((X[7,8]-mean(X[,8]))^2)## x9
## -1(X[8,8]-mean(X[,8]))/sqrt((X[8,8]-mean(X[,8]))^2)## x9
## 1(X[9,8]-mean(X[,8]))/sqrt((X[9,8]-mean(X[,8]))^2)## x9
## -1(X[10,8]-mean(X[,8]))/sqrt((X[10,8]-mean(X[,8]))^2)## x9
## -1(X[11,8]-mean(X[,8]))/sqrt((X[11,8]-mean(X[,8]))^2)## x9
## -1(X[12,8]-mean(X[,8]))/sqrt((X[12,8]-mean(X[,8]))^2)## x9
## -1(X[13,8]-mean(X[,8]))/sqrt((X[13,8]-mean(X[,8]))^2)## x9
## -1(X[14,8]-mean(X[,8]))/sqrt((X[14,8]-mean(X[,8]))^2)## x9
## -1(X[15,8]-mean(X[,8]))/sqrt((X[15,8]-mean(X[,8]))^2)## x9
## 1(X[16,8]-mean(X[,8]))/sqrt((X[16,8]-mean(X[,8]))^2)## x9
## 1(X[17,8]-mean(X[,8]))/sqrt((X[17,8]-mean(X[,8]))^2)## x9
## 1(X[18,8]-mean(X[,8]))/sqrt((X[18,8]-mean(X[,8]))^2)## x9
## 1(X[19,8]-mean(X[,8]))/sqrt((X[19,8]-mean(X[,8]))^2)## x9
## 1(X[20,8]-mean(X[,8]))/sqrt((X[20,8]-mean(X[,8]))^2)## x9
## 1(X[21,8]-mean(X[,8]))/sqrt((X[21,8]-mean(X[,8]))^2)## x9
## 1(X[22,8]-mean(X[,8]))/sqrt((X[22,8]-mean(X[,8]))^2)## x9
## -1(X[23,8]-mean(X[,8]))/sqrt((X[23,8]-mean(X[,8]))^2)## x9
## 1(X[24,8]-mean(X[,8]))/sqrt((X[24,8]-mean(X[,8]))^2)## x9
## -1(X[25,8]-mean(X[,8]))/sqrt((X[25,8]-mean(X[,8]))^2)## x9
## 1(X[26,8]-mean(X[,8]))/sqrt((X[26,8]-mean(X[,8]))^2)## x9
## -1(X[27,8]-mean(X[,8]))/sqrt((X[27,8]-mean(X[,8]))^2)## x9
## -1(X[28,8]-mean(X[,8]))/sqrt((X[28,8]-mean(X[,8]))^2)## x9
## -1(X[29,8]-mean(X[,8]))/sqrt((X[29,8]-mean(X[,8]))^2)## x9
## 1(X[30,8]-mean(X[,8]))/sqrt((X[30,8]-mean(X[,8]))^2)## x9
## -1(X[31,8]-mean(X[,8]))/sqrt((X[31,8]-mean(X[,8]))^2)## x9
## -1(X[32,8]-mean(X[,8]))/sqrt((X[32,8]-mean(X[,8]))^2)## x9
## -1Next, W will be created with the unit length scaling results
W<-cbind(1, c(1,-1,1,1,1,1,1,-1,1,-1,1,-1,1,1,1,1,-1,-1,1,1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1), c(-1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,-1,1,1,-1,1,-1,1,1,-1,-1,1),c(1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,-1,1,-1,1,-1,-1,-1,1,1,-1,-1), c(1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,-1,1,-1,1,-1,-1,-1,1,1,-1,1), c(-1,-1,1,-1,1,1,-1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,1,-1,1,1,-1,-1,-1,-1,-1,1,-1,1,-1,1), c(1,1,1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,-1,1,-1,1,-1,-1,-1,1,-1,-1,-1))Now the length scaling correlation matrix ofW^TW is processed and compared to the correlation matrix of X to show similarities and if it indicates signs of colinerarity The results obtained show no similarity to each other, with the correlation of matrix X being much closer to the W matrix than the correlated WTW matrix. Most likely the result of error, but could also indicate that the matrices don’t have as musch in common since they are each dedicated to a completely different part of the wine’s quality
W## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 1 1 -1 1 1 -1 1
## [2,] 1 -1 -1 1 1 -1 1
## [3,] 1 1 -1 1 1 1 1
## [4,] 1 1 1 1 1 -1 1
## [5,] 1 1 -1 1 1 1 -1
## [6,] 1 1 -1 1 1 1 1
## [7,] 1 1 -1 -1 -1 -1 -1
## [8,] 1 -1 -1 -1 -1 -1 1
## [9,] 1 1 -1 -1 -1 1 -1
## [10,] 1 -1 1 -1 -1 -1 -1
## [11,] 1 1 -1 -1 -1 -1 -1
## [12,] 1 -1 1 -1 -1 1 -1
## [13,] 1 1 -1 -1 -1 1 -1
## [14,] 1 1 1 -1 -1 -1 -1
## [15,] 1 1 -1 -1 1 1 1
## [16,] 1 1 -1 1 1 1 1
## [17,] 1 -1 -1 1 1 -1 1
## [18,] 1 -1 -1 1 1 -1 1
## [19,] 1 1 -1 1 1 1 1
## [20,] 1 1 -1 1 1 -1 1
## [21,] 1 -1 1 1 1 1 1
## [22,] 1 1 -1 -1 -1 1 -1
## [23,] 1 -1 1 1 1 -1 1
## [24,] 1 -1 1 -1 -1 -1 -1
## [25,] 1 -1 -1 1 1 -1 1
## [26,] 1 -1 1 -1 -1 -1 -1
## [27,] 1 1 -1 -1 -1 -1 -1
## [28,] 1 -1 1 -1 -1 1 -1
## [29,] 1 -1 1 1 1 -1 1
## [30,] 1 1 -1 1 1 1 -1
## [31,] 1 -1 -1 -1 -1 -1 -1
## [32,] 1 -1 1 -1 1 1 -1t(W)%*%W## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 32 2 -10 0 4 -4 0
## [2,] 2 32 -16 2 2 10 -2
## [3,] -10 -16 32 -6 -6 -2 -6
## [4,] 0 2 -6 32 28 0 24
## [5,] 4 2 -6 28 32 4 24
## [6,] -4 10 -2 0 4 32 -4
## [7,] 0 -2 -6 24 24 -4 32cor(X[-1, -1])## x2 x3 x4 x6 x7 x8
## x2 1.00000000 -0.5806522 0.20802464 0.21526202 0.08022391 0.10109556
## x3 -0.58065221 1.0000000 -0.38198932 -0.31421118 -0.36026198 0.39850335
## x4 0.20802464 -0.3819893 1.00000000 0.94391462 0.93554052 0.03200615
## x6 0.21526202 -0.3142112 0.94391462 1.00000000 0.77481412 -0.02645929
## x7 0.08022391 -0.3602620 0.93554052 0.77481412 1.00000000 0.05152066
## x8 0.10109556 0.3985034 0.03200615 -0.02645929 0.05152066 1.00000000
## x9 -0.05697365 -0.4888703 0.79205675 0.68283166 0.84411036 -0.44837351
## x9
## x2 -0.05697365
## x3 -0.48887030
## x4 0.79205675
## x6 0.68283166
## x7 0.84411036
## x8 -0.44837351
## x9 1.00000000This displays the eigenvector and eigenvalue of the W matrix. Then a manual check by multiplying WTW by each of the generated eigenvectors.
eigen(t(W)%*%W)## eigen() decomposition
## $values
## [1] 85.586727 52.045588 38.744747 23.638622 13.176761 7.662141 3.145413
##
## $vectors
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -0.08823816 -0.25826896 0.68116180 0.62577626 0.1830788 0.1264359
## [2,] -0.10025430 -0.65192460 -0.17125486 -0.31794159 0.6266893 0.2038857
## [3,] 0.23390184 0.56045598 -0.27150184 0.31720891 0.6384250 0.2152630
## [4,] -0.56565562 0.12729541 -0.09348408 -0.02255525 0.1765521 -0.4820450
## [5,] -0.57115537 0.07609504 -0.08928969 0.22281572 0.1289914 -0.2153164
## [6,] -0.02393855 -0.35671896 -0.64472859 0.57891064 -0.2921922 0.1177636
## [7,] -0.52980679 0.21198480 0.02429515 -0.14629627 -0.1815779 0.7768588
## [,7]
## [1,] 0.14293337
## [2,] -0.01481522
## [3,] 0.05403386
## [4,] 0.62533473
## [5,] -0.73984570
## [6,] 0.14873288
## [7,] 0.12607242(t(W)%*%W)*-0.08823816## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -2.8236211 -0.1764763 0.8823816 0.0000000 -0.3529526 0.3529526
## [2,] -0.1764763 -2.8236211 1.4118106 -0.1764763 -0.1764763 -0.8823816
## [3,] 0.8823816 1.4118106 -2.8236211 0.5294290 0.5294290 0.1764763
## [4,] 0.0000000 -0.1764763 0.5294290 -2.8236211 -2.4706685 0.0000000
## [5,] -0.3529526 -0.1764763 0.5294290 -2.4706685 -2.8236211 -0.3529526
## [6,] 0.3529526 -0.8823816 0.1764763 0.0000000 -0.3529526 -2.8236211
## [7,] 0.0000000 0.1764763 0.5294290 -2.1177158 -2.1177158 0.3529526
## [,7]
## [1,] 0.0000000
## [2,] 0.1764763
## [3,] 0.5294290
## [4,] -2.1177158
## [5,] -2.1177158
## [6,] 0.3529526
## [7,] -2.8236211(t(W)%*%W)*-0.10025430## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -3.2081376 -0.2005086 1.0025430 0.0000000 -0.4010172 0.4010172
## [2,] -0.2005086 -3.2081376 1.6040688 -0.2005086 -0.2005086 -1.0025430
## [3,] 1.0025430 1.6040688 -3.2081376 0.6015258 0.6015258 0.2005086
## [4,] 0.0000000 -0.2005086 0.6015258 -3.2081376 -2.8071204 0.0000000
## [5,] -0.4010172 -0.2005086 0.6015258 -2.8071204 -3.2081376 -0.4010172
## [6,] 0.4010172 -1.0025430 0.2005086 0.0000000 -0.4010172 -3.2081376
## [7,] 0.0000000 0.2005086 0.6015258 -2.4061032 -2.4061032 0.4010172
## [,7]
## [1,] 0.0000000
## [2,] 0.2005086
## [3,] 0.6015258
## [4,] -2.4061032
## [5,] -2.4061032
## [6,] 0.4010172
## [7,] -3.2081376(t(W)%*%W)*0.23390184## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 7.4848589 0.4678037 -2.3390184 0.0000000 0.9356074 -0.9356074
## [2,] 0.4678037 7.4848589 -3.7424294 0.4678037 0.4678037 2.3390184
## [3,] -2.3390184 -3.7424294 7.4848589 -1.4034110 -1.4034110 -0.4678037
## [4,] 0.0000000 0.4678037 -1.4034110 7.4848589 6.5492515 0.0000000
## [5,] 0.9356074 0.4678037 -1.4034110 6.5492515 7.4848589 0.9356074
## [6,] -0.9356074 2.3390184 -0.4678037 0.0000000 0.9356074 7.4848589
## [7,] 0.0000000 -0.4678037 -1.4034110 5.6136442 5.6136442 -0.9356074
## [,7]
## [1,] 0.0000000
## [2,] -0.4678037
## [3,] -1.4034110
## [4,] 5.6136442
## [5,] 5.6136442
## [6,] -0.9356074
## [7,] 7.4848589(t(W)%*%W)*-0.56565562## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -18.100980 -1.131311 5.656556 0.000000 -2.262622 2.262622
## [2,] -1.131311 -18.100980 9.050490 -1.131311 -1.131311 -5.656556
## [3,] 5.656556 9.050490 -18.100980 3.393934 3.393934 1.131311
## [4,] 0.000000 -1.131311 3.393934 -18.100980 -15.838357 0.000000
## [5,] -2.262622 -1.131311 3.393934 -15.838357 -18.100980 -2.262622
## [6,] 2.262622 -5.656556 1.131311 0.000000 -2.262622 -18.100980
## [7,] 0.000000 1.131311 3.393934 -13.575735 -13.575735 2.262622
## [,7]
## [1,] 0.000000
## [2,] 1.131311
## [3,] 3.393934
## [4,] -13.575735
## [5,] -13.575735
## [6,] 2.262622
## [7,] -18.100980(t(W)%*%W)*-0.57115537## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -18.276972 -1.142311 5.711554 0.000000 -2.284621 2.284621
## [2,] -1.142311 -18.276972 9.138486 -1.142311 -1.142311 -5.711554
## [3,] 5.711554 9.138486 -18.276972 3.426932 3.426932 1.142311
## [4,] 0.000000 -1.142311 3.426932 -18.276972 -15.992350 0.000000
## [5,] -2.284621 -1.142311 3.426932 -15.992350 -18.276972 -2.284621
## [6,] 2.284621 -5.711554 1.142311 0.000000 -2.284621 -18.276972
## [7,] 0.000000 1.142311 3.426932 -13.707729 -13.707729 2.284621
## [,7]
## [1,] 0.000000
## [2,] 1.142311
## [3,] 3.426932
## [4,] -13.707729
## [5,] -13.707729
## [6,] 2.284621
## [7,] -18.276972(t(W)%*%W)*-0.02393855## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -0.7660336 -0.0478771 0.2393855 0.0000000 -0.0957542 0.0957542
## [2,] -0.0478771 -0.7660336 0.3830168 -0.0478771 -0.0478771 -0.2393855
## [3,] 0.2393855 0.3830168 -0.7660336 0.1436313 0.1436313 0.0478771
## [4,] 0.0000000 -0.0478771 0.1436313 -0.7660336 -0.6702794 0.0000000
## [5,] -0.0957542 -0.0478771 0.1436313 -0.6702794 -0.7660336 -0.0957542
## [6,] 0.0957542 -0.2393855 0.0478771 0.0000000 -0.0957542 -0.7660336
## [7,] 0.0000000 0.0478771 0.1436313 -0.5745252 -0.5745252 0.0957542
## [,7]
## [1,] 0.0000000
## [2,] 0.0478771
## [3,] 0.1436313
## [4,] -0.5745252
## [5,] -0.5745252
## [6,] 0.0957542
## [7,] -0.7660336(t(W)%*%W)*-0.52980679## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -16.953817 -1.059614 5.298068 0.000000 -2.119227 2.119227
## [2,] -1.059614 -16.953817 8.476909 -1.059614 -1.059614 -5.298068
## [3,] 5.298068 8.476909 -16.953817 3.178841 3.178841 1.059614
## [4,] 0.000000 -1.059614 3.178841 -16.953817 -14.834590 0.000000
## [5,] -2.119227 -1.059614 3.178841 -14.834590 -16.953817 -2.119227
## [6,] 2.119227 -5.298068 1.059614 0.000000 -2.119227 -16.953817
## [7,] 0.000000 1.059614 3.178841 -12.715363 -12.715363 2.119227
## [,7]
## [1,] 0.000000
## [2,] 1.059614
## [3,] 3.178841
## [4,] -12.715363
## [5,] -12.715363
## [6,] 2.119227
## [7,] -16.953817(t(W)%*%W)*-0.25826896## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -8.2646067 -0.5165379 2.5826896 0.0000000 -1.0330758 1.0330758
## [2,] -0.5165379 -8.2646067 4.1323034 -0.5165379 -0.5165379 -2.5826896
## [3,] 2.5826896 4.1323034 -8.2646067 1.5496138 1.5496138 0.5165379
## [4,] 0.0000000 -0.5165379 1.5496138 -8.2646067 -7.2315309 0.0000000
## [5,] -1.0330758 -0.5165379 1.5496138 -7.2315309 -8.2646067 -1.0330758
## [6,] 1.0330758 -2.5826896 0.5165379 0.0000000 -1.0330758 -8.2646067
## [7,] 0.0000000 0.5165379 1.5496138 -6.1984550 -6.1984550 1.0330758
## [,7]
## [1,] 0.0000000
## [2,] 0.5165379
## [3,] 1.5496138
## [4,] -6.1984550
## [5,] -6.1984550
## [6,] 1.0330758
## [7,] -8.2646067(t(W)%*%W)*-0.65192460## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -20.861587 -1.303849 6.519246 0.000000 -2.607698 2.607698
## [2,] -1.303849 -20.861587 10.430794 -1.303849 -1.303849 -6.519246
## [3,] 6.519246 10.430794 -20.861587 3.911548 3.911548 1.303849
## [4,] 0.000000 -1.303849 3.911548 -20.861587 -18.253889 0.000000
## [5,] -2.607698 -1.303849 3.911548 -18.253889 -20.861587 -2.607698
## [6,] 2.607698 -6.519246 1.303849 0.000000 -2.607698 -20.861587
## [7,] 0.000000 1.303849 3.911548 -15.646190 -15.646190 2.607698
## [,7]
## [1,] 0.000000
## [2,] 1.303849
## [3,] 3.911548
## [4,] -15.646190
## [5,] -15.646190
## [6,] 2.607698
## [7,] -20.861587(t(W)%*%W)*0.56045598## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 17.934591 1.120912 -5.604560 0.000000 2.241824 -2.241824 0.000000
## [2,] 1.120912 17.934591 -8.967296 1.120912 1.120912 5.604560 -1.120912
## [3,] -5.604560 -8.967296 17.934591 -3.362736 -3.362736 -1.120912 -3.362736
## [4,] 0.000000 1.120912 -3.362736 17.934591 15.692767 0.000000 13.450944
## [5,] 2.241824 1.120912 -3.362736 15.692767 17.934591 2.241824 13.450944
## [6,] -2.241824 5.604560 -1.120912 0.000000 2.241824 17.934591 -2.241824
## [7,] 0.000000 -1.120912 -3.362736 13.450944 13.450944 -2.241824 17.934591(t(W)%*%W)*0.12729541## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 4.0734531 0.2545908 -1.2729541 0.0000000 0.5091816 -0.5091816
## [2,] 0.2545908 4.0734531 -2.0367266 0.2545908 0.2545908 1.2729541
## [3,] -1.2729541 -2.0367266 4.0734531 -0.7637725 -0.7637725 -0.2545908
## [4,] 0.0000000 0.2545908 -0.7637725 4.0734531 3.5642715 0.0000000
## [5,] 0.5091816 0.2545908 -0.7637725 3.5642715 4.0734531 0.5091816
## [6,] -0.5091816 1.2729541 -0.2545908 0.0000000 0.5091816 4.0734531
## [7,] 0.0000000 -0.2545908 -0.7637725 3.0550898 3.0550898 -0.5091816
## [,7]
## [1,] 0.0000000
## [2,] -0.2545908
## [3,] -0.7637725
## [4,] 3.0550898
## [5,] 3.0550898
## [6,] -0.5091816
## [7,] 4.0734531(t(W)%*%W)*0.07609504## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 2.4350413 0.1521901 -0.7609504 0.0000000 0.3043802 -0.3043802
## [2,] 0.1521901 2.4350413 -1.2175206 0.1521901 0.1521901 0.7609504
## [3,] -0.7609504 -1.2175206 2.4350413 -0.4565702 -0.4565702 -0.1521901
## [4,] 0.0000000 0.1521901 -0.4565702 2.4350413 2.1306611 0.0000000
## [5,] 0.3043802 0.1521901 -0.4565702 2.1306611 2.4350413 0.3043802
## [6,] -0.3043802 0.7609504 -0.1521901 0.0000000 0.3043802 2.4350413
## [7,] 0.0000000 -0.1521901 -0.4565702 1.8262810 1.8262810 -0.3043802
## [,7]
## [1,] 0.0000000
## [2,] -0.1521901
## [3,] -0.4565702
## [4,] 1.8262810
## [5,] 1.8262810
## [6,] -0.3043802
## [7,] 2.4350413(t(W)%*%W)*-0.35671896## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -11.4150067 -0.7134379 3.5671896 0.0000000 -1.4268758 1.4268758
## [2,] -0.7134379 -11.4150067 5.7075034 -0.7134379 -0.7134379 -3.5671896
## [3,] 3.5671896 5.7075034 -11.4150067 2.1403138 2.1403138 0.7134379
## [4,] 0.0000000 -0.7134379 2.1403138 -11.4150067 -9.9881309 0.0000000
## [5,] -1.4268758 -0.7134379 2.1403138 -9.9881309 -11.4150067 -1.4268758
## [6,] 1.4268758 -3.5671896 0.7134379 0.0000000 -1.4268758 -11.4150067
## [7,] 0.0000000 0.7134379 2.1403138 -8.5612550 -8.5612550 1.4268758
## [,7]
## [1,] 0.0000000
## [2,] 0.7134379
## [3,] 2.1403138
## [4,] -8.5612550
## [5,] -8.5612550
## [6,] 1.4268758
## [7,] -11.4150067(t(W)%*%W)*0.21198480## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 6.7835136 0.4239696 -2.1198480 0.0000000 0.8479392 -0.8479392
## [2,] 0.4239696 6.7835136 -3.3917568 0.4239696 0.4239696 2.1198480
## [3,] -2.1198480 -3.3917568 6.7835136 -1.2719088 -1.2719088 -0.4239696
## [4,] 0.0000000 0.4239696 -1.2719088 6.7835136 5.9355744 0.0000000
## [5,] 0.8479392 0.4239696 -1.2719088 5.9355744 6.7835136 0.8479392
## [6,] -0.8479392 2.1198480 -0.4239696 0.0000000 0.8479392 6.7835136
## [7,] 0.0000000 -0.4239696 -1.2719088 5.0876352 5.0876352 -0.8479392
## [,7]
## [1,] 0.0000000
## [2,] -0.4239696
## [3,] -1.2719088
## [4,] 5.0876352
## [5,] 5.0876352
## [6,] -0.8479392
## [7,] 6.7835136(t(W)%*%W)*0.68116180## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 21.797178 1.362324 -6.811618 0.000000 2.724647 -2.724647 0.000000
## [2,] 1.362324 21.797178 -10.898589 1.362324 1.362324 6.811618 -1.362324
## [3,] -6.811618 -10.898589 21.797178 -4.086971 -4.086971 -1.362324 -4.086971
## [4,] 0.000000 1.362324 -4.086971 21.797178 19.072530 0.000000 16.347883
## [5,] 2.724647 1.362324 -4.086971 19.072530 21.797178 2.724647 16.347883
## [6,] -2.724647 6.811618 -1.362324 0.000000 2.724647 21.797178 -2.724647
## [7,] 0.000000 -1.362324 -4.086971 16.347883 16.347883 -2.724647 21.797178(t(W)%*%W)*-0.17125486## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -5.4801555 -0.3425097 1.7125486 0.0000000 -0.6850194 0.6850194
## [2,] -0.3425097 -5.4801555 2.7400778 -0.3425097 -0.3425097 -1.7125486
## [3,] 1.7125486 2.7400778 -5.4801555 1.0275292 1.0275292 0.3425097
## [4,] 0.0000000 -0.3425097 1.0275292 -5.4801555 -4.7951361 0.0000000
## [5,] -0.6850194 -0.3425097 1.0275292 -4.7951361 -5.4801555 -0.6850194
## [6,] 0.6850194 -1.7125486 0.3425097 0.0000000 -0.6850194 -5.4801555
## [7,] 0.0000000 0.3425097 1.0275292 -4.1101166 -4.1101166 0.6850194
## [,7]
## [1,] 0.0000000
## [2,] 0.3425097
## [3,] 1.0275292
## [4,] -4.1101166
## [5,] -4.1101166
## [6,] 0.6850194
## [7,] -5.4801555(t(W)%*%W)*-0.27150184## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -8.6880589 -0.5430037 2.7150184 0.0000000 -1.0860074 1.0860074
## [2,] -0.5430037 -8.6880589 4.3440294 -0.5430037 -0.5430037 -2.7150184
## [3,] 2.7150184 4.3440294 -8.6880589 1.6290110 1.6290110 0.5430037
## [4,] 0.0000000 -0.5430037 1.6290110 -8.6880589 -7.6020515 0.0000000
## [5,] -1.0860074 -0.5430037 1.6290110 -7.6020515 -8.6880589 -1.0860074
## [6,] 1.0860074 -2.7150184 0.5430037 0.0000000 -1.0860074 -8.6880589
## [7,] 0.0000000 0.5430037 1.6290110 -6.5160442 -6.5160442 1.0860074
## [,7]
## [1,] 0.0000000
## [2,] 0.5430037
## [3,] 1.6290110
## [4,] -6.5160442
## [5,] -6.5160442
## [6,] 1.0860074
## [7,] -8.6880589(t(W)%*%W)*-0.09348408## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -2.9914906 -0.1869682 0.9348408 0.0000000 -0.3739363 0.3739363
## [2,] -0.1869682 -2.9914906 1.4957453 -0.1869682 -0.1869682 -0.9348408
## [3,] 0.9348408 1.4957453 -2.9914906 0.5609045 0.5609045 0.1869682
## [4,] 0.0000000 -0.1869682 0.5609045 -2.9914906 -2.6175542 0.0000000
## [5,] -0.3739363 -0.1869682 0.5609045 -2.6175542 -2.9914906 -0.3739363
## [6,] 0.3739363 -0.9348408 0.1869682 0.0000000 -0.3739363 -2.9914906
## [7,] 0.0000000 0.1869682 0.5609045 -2.2436179 -2.2436179 0.3739363
## [,7]
## [1,] 0.0000000
## [2,] 0.1869682
## [3,] 0.5609045
## [4,] -2.2436179
## [5,] -2.2436179
## [6,] 0.3739363
## [7,] -2.9914906(t(W)%*%W)*-0.08928969## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -2.8572701 -0.1785794 0.8928969 0.0000000 -0.3571588 0.3571588
## [2,] -0.1785794 -2.8572701 1.4286350 -0.1785794 -0.1785794 -0.8928969
## [3,] 0.8928969 1.4286350 -2.8572701 0.5357381 0.5357381 0.1785794
## [4,] 0.0000000 -0.1785794 0.5357381 -2.8572701 -2.5001113 0.0000000
## [5,] -0.3571588 -0.1785794 0.5357381 -2.5001113 -2.8572701 -0.3571588
## [6,] 0.3571588 -0.8928969 0.1785794 0.0000000 -0.3571588 -2.8572701
## [7,] 0.0000000 0.1785794 0.5357381 -2.1429526 -2.1429526 0.3571588
## [,7]
## [1,] 0.0000000
## [2,] 0.1785794
## [3,] 0.5357381
## [4,] -2.1429526
## [5,] -2.1429526
## [6,] 0.3571588
## [7,] -2.8572701(t(W)%*%W)*-0.64472859## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -20.631315 -1.289457 6.447286 0.000000 -2.578914 2.578914
## [2,] -1.289457 -20.631315 10.315657 -1.289457 -1.289457 -6.447286
## [3,] 6.447286 10.315657 -20.631315 3.868372 3.868372 1.289457
## [4,] 0.000000 -1.289457 3.868372 -20.631315 -18.052401 0.000000
## [5,] -2.578914 -1.289457 3.868372 -18.052401 -20.631315 -2.578914
## [6,] 2.578914 -6.447286 1.289457 0.000000 -2.578914 -20.631315
## [7,] 0.000000 1.289457 3.868372 -15.473486 -15.473486 2.578914
## [,7]
## [1,] 0.000000
## [2,] 1.289457
## [3,] 3.868372
## [4,] -15.473486
## [5,] -15.473486
## [6,] 2.578914
## [7,] -20.631315(t(W)%*%W)*0.02429515## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.7774448 0.0485903 -0.2429515 0.0000000 0.0971806 -0.0971806
## [2,] 0.0485903 0.7774448 -0.3887224 0.0485903 0.0485903 0.2429515
## [3,] -0.2429515 -0.3887224 0.7774448 -0.1457709 -0.1457709 -0.0485903
## [4,] 0.0000000 0.0485903 -0.1457709 0.7774448 0.6802642 0.0000000
## [5,] 0.0971806 0.0485903 -0.1457709 0.6802642 0.7774448 0.0971806
## [6,] -0.0971806 0.2429515 -0.0485903 0.0000000 0.0971806 0.7774448
## [7,] 0.0000000 -0.0485903 -0.1457709 0.5830836 0.5830836 -0.0971806
## [,7]
## [1,] 0.0000000
## [2,] -0.0485903
## [3,] -0.1457709
## [4,] 0.5830836
## [5,] 0.5830836
## [6,] -0.0971806
## [7,] 0.7774448(t(W)%*%W)*0.62577626## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 20.024840 1.251553 -6.257763 0.000000 2.503105 -2.503105 0.000000
## [2,] 1.251553 20.024840 -10.012420 1.251553 1.251553 6.257763 -1.251553
## [3,] -6.257763 -10.012420 20.024840 -3.754658 -3.754658 -1.251553 -3.754658
## [4,] 0.000000 1.251553 -3.754658 20.024840 17.521735 0.000000 15.018630
## [5,] 2.503105 1.251553 -3.754658 17.521735 20.024840 2.503105 15.018630
## [6,] -2.503105 6.257763 -1.251553 0.000000 2.503105 20.024840 -2.503105
## [7,] 0.000000 -1.251553 -3.754658 15.018630 15.018630 -2.503105 20.024840(t(W)%*%W)*-0.31794159## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -10.1741309 -0.6358832 3.1794159 0.0000000 -1.2717664 1.2717664
## [2,] -0.6358832 -10.1741309 5.0870654 -0.6358832 -0.6358832 -3.1794159
## [3,] 3.1794159 5.0870654 -10.1741309 1.9076495 1.9076495 0.6358832
## [4,] 0.0000000 -0.6358832 1.9076495 -10.1741309 -8.9023645 0.0000000
## [5,] -1.2717664 -0.6358832 1.9076495 -8.9023645 -10.1741309 -1.2717664
## [6,] 1.2717664 -3.1794159 0.6358832 0.0000000 -1.2717664 -10.1741309
## [7,] 0.0000000 0.6358832 1.9076495 -7.6305982 -7.6305982 1.2717664
## [,7]
## [1,] 0.0000000
## [2,] 0.6358832
## [3,] 1.9076495
## [4,] -7.6305982
## [5,] -7.6305982
## [6,] 1.2717664
## [7,] -10.1741309(t(W)%*%W)*0.31720891## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 10.1506851 0.6344178 -3.1720891 0.0000000 1.2688356 -1.2688356
## [2,] 0.6344178 10.1506851 -5.0753426 0.6344178 0.6344178 3.1720891
## [3,] -3.1720891 -5.0753426 10.1506851 -1.9032535 -1.9032535 -0.6344178
## [4,] 0.0000000 0.6344178 -1.9032535 10.1506851 8.8818495 0.0000000
## [5,] 1.2688356 0.6344178 -1.9032535 8.8818495 10.1506851 1.2688356
## [6,] -1.2688356 3.1720891 -0.6344178 0.0000000 1.2688356 10.1506851
## [7,] 0.0000000 -0.6344178 -1.9032535 7.6130138 7.6130138 -1.2688356
## [,7]
## [1,] 0.0000000
## [2,] -0.6344178
## [3,] -1.9032535
## [4,] 7.6130138
## [5,] 7.6130138
## [6,] -1.2688356
## [7,] 10.1506851(t(W)%*%W)*-0.02255525## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -0.7217680 -0.0451105 0.2255525 0.0000000 -0.0902210 0.0902210
## [2,] -0.0451105 -0.7217680 0.3608840 -0.0451105 -0.0451105 -0.2255525
## [3,] 0.2255525 0.3608840 -0.7217680 0.1353315 0.1353315 0.0451105
## [4,] 0.0000000 -0.0451105 0.1353315 -0.7217680 -0.6315470 0.0000000
## [5,] -0.0902210 -0.0451105 0.1353315 -0.6315470 -0.7217680 -0.0902210
## [6,] 0.0902210 -0.2255525 0.0451105 0.0000000 -0.0902210 -0.7217680
## [7,] 0.0000000 0.0451105 0.1353315 -0.5413260 -0.5413260 0.0902210
## [,7]
## [1,] 0.0000000
## [2,] 0.0451105
## [3,] 0.1353315
## [4,] -0.5413260
## [5,] -0.5413260
## [6,] 0.0902210
## [7,] -0.7217680(t(W)%*%W)*0.22281572## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 7.1301030 0.4456314 -2.2281572 0.0000000 0.8912629 -0.8912629
## [2,] 0.4456314 7.1301030 -3.5650515 0.4456314 0.4456314 2.2281572
## [3,] -2.2281572 -3.5650515 7.1301030 -1.3368943 -1.3368943 -0.4456314
## [4,] 0.0000000 0.4456314 -1.3368943 7.1301030 6.2388402 0.0000000
## [5,] 0.8912629 0.4456314 -1.3368943 6.2388402 7.1301030 0.8912629
## [6,] -0.8912629 2.2281572 -0.4456314 0.0000000 0.8912629 7.1301030
## [7,] 0.0000000 -0.4456314 -1.3368943 5.3475773 5.3475773 -0.8912629
## [,7]
## [1,] 0.0000000
## [2,] -0.4456314
## [3,] -1.3368943
## [4,] 5.3475773
## [5,] 5.3475773
## [6,] -0.8912629
## [7,] 7.1301030(t(W)%*%W)*0.57891064## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 18.525140 1.157821 -5.789106 0.000000 2.315643 -2.315643 0.000000
## [2,] 1.157821 18.525140 -9.262570 1.157821 1.157821 5.789106 -1.157821
## [3,] -5.789106 -9.262570 18.525140 -3.473464 -3.473464 -1.157821 -3.473464
## [4,] 0.000000 1.157821 -3.473464 18.525140 16.209498 0.000000 13.893855
## [5,] 2.315643 1.157821 -3.473464 16.209498 18.525140 2.315643 13.893855
## [6,] -2.315643 5.789106 -1.157821 0.000000 2.315643 18.525140 -2.315643
## [7,] 0.000000 -1.157821 -3.473464 13.893855 13.893855 -2.315643 18.525140(t(W)%*%W)*-0.14629627## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -4.6814806 -0.2925925 1.4629627 0.0000000 -0.5851851 0.5851851
## [2,] -0.2925925 -4.6814806 2.3407403 -0.2925925 -0.2925925 -1.4629627
## [3,] 1.4629627 2.3407403 -4.6814806 0.8777776 0.8777776 0.2925925
## [4,] 0.0000000 -0.2925925 0.8777776 -4.6814806 -4.0962956 0.0000000
## [5,] -0.5851851 -0.2925925 0.8777776 -4.0962956 -4.6814806 -0.5851851
## [6,] 0.5851851 -1.4629627 0.2925925 0.0000000 -0.5851851 -4.6814806
## [7,] 0.0000000 0.2925925 0.8777776 -3.5111105 -3.5111105 0.5851851
## [,7]
## [1,] 0.0000000
## [2,] 0.2925925
## [3,] 0.8777776
## [4,] -3.5111105
## [5,] -3.5111105
## [6,] 0.5851851
## [7,] -4.6814806(t(W)%*%W)*0.1830788## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 5.8585216 0.3661576 -1.8307880 0.0000000 0.7323152 -0.7323152
## [2,] 0.3661576 5.8585216 -2.9292608 0.3661576 0.3661576 1.8307880
## [3,] -1.8307880 -2.9292608 5.8585216 -1.0984728 -1.0984728 -0.3661576
## [4,] 0.0000000 0.3661576 -1.0984728 5.8585216 5.1262064 0.0000000
## [5,] 0.7323152 0.3661576 -1.0984728 5.1262064 5.8585216 0.7323152
## [6,] -0.7323152 1.8307880 -0.3661576 0.0000000 0.7323152 5.8585216
## [7,] 0.0000000 -0.3661576 -1.0984728 4.3938912 4.3938912 -0.7323152
## [,7]
## [1,] 0.0000000
## [2,] -0.3661576
## [3,] -1.0984728
## [4,] 4.3938912
## [5,] 4.3938912
## [6,] -0.7323152
## [7,] 5.8585216(t(W)%*%W)*0.6266893## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 20.054058 1.253379 -6.266893 0.000000 2.506757 -2.506757 0.000000
## [2,] 1.253379 20.054058 -10.027029 1.253379 1.253379 6.266893 -1.253379
## [3,] -6.266893 -10.027029 20.054058 -3.760136 -3.760136 -1.253379 -3.760136
## [4,] 0.000000 1.253379 -3.760136 20.054058 17.547300 0.000000 15.040543
## [5,] 2.506757 1.253379 -3.760136 17.547300 20.054058 2.506757 15.040543
## [6,] -2.506757 6.266893 -1.253379 0.000000 2.506757 20.054058 -2.506757
## [7,] 0.000000 -1.253379 -3.760136 15.040543 15.040543 -2.506757 20.054058(t(W)%*%W)*0.6384250## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 20.42960 1.27685 -6.38425 0.00000 2.55370 -2.55370 0.00000
## [2,] 1.27685 20.42960 -10.21480 1.27685 1.27685 6.38425 -1.27685
## [3,] -6.38425 -10.21480 20.42960 -3.83055 -3.83055 -1.27685 -3.83055
## [4,] 0.00000 1.27685 -3.83055 20.42960 17.87590 0.00000 15.32220
## [5,] 2.55370 1.27685 -3.83055 17.87590 20.42960 2.55370 15.32220
## [6,] -2.55370 6.38425 -1.27685 0.00000 2.55370 20.42960 -2.55370
## [7,] 0.00000 -1.27685 -3.83055 15.32220 15.32220 -2.55370 20.42960(t(W)%*%W)*0.1765521## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 5.6496672 0.3531042 -1.7655210 0.0000000 0.7062084 -0.7062084
## [2,] 0.3531042 5.6496672 -2.8248336 0.3531042 0.3531042 1.7655210
## [3,] -1.7655210 -2.8248336 5.6496672 -1.0593126 -1.0593126 -0.3531042
## [4,] 0.0000000 0.3531042 -1.0593126 5.6496672 4.9434588 0.0000000
## [5,] 0.7062084 0.3531042 -1.0593126 4.9434588 5.6496672 0.7062084
## [6,] -0.7062084 1.7655210 -0.3531042 0.0000000 0.7062084 5.6496672
## [7,] 0.0000000 -0.3531042 -1.0593126 4.2372504 4.2372504 -0.7062084
## [,7]
## [1,] 0.0000000
## [2,] -0.3531042
## [3,] -1.0593126
## [4,] 4.2372504
## [5,] 4.2372504
## [6,] -0.7062084
## [7,] 5.6496672(t(W)%*%W)*0.1289914## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 4.1277248 0.2579828 -1.2899140 0.0000000 0.5159656 -0.5159656
## [2,] 0.2579828 4.1277248 -2.0638624 0.2579828 0.2579828 1.2899140
## [3,] -1.2899140 -2.0638624 4.1277248 -0.7739484 -0.7739484 -0.2579828
## [4,] 0.0000000 0.2579828 -0.7739484 4.1277248 3.6117592 0.0000000
## [5,] 0.5159656 0.2579828 -0.7739484 3.6117592 4.1277248 0.5159656
## [6,] -0.5159656 1.2899140 -0.2579828 0.0000000 0.5159656 4.1277248
## [7,] 0.0000000 -0.2579828 -0.7739484 3.0957936 3.0957936 -0.5159656
## [,7]
## [1,] 0.0000000
## [2,] -0.2579828
## [3,] -0.7739484
## [4,] 3.0957936
## [5,] 3.0957936
## [6,] -0.5159656
## [7,] 4.1277248(t(W)%*%W)*-0.2921922## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -9.3501504 -0.5843844 2.9219220 0.0000000 -1.1687688 1.1687688
## [2,] -0.5843844 -9.3501504 4.6750752 -0.5843844 -0.5843844 -2.9219220
## [3,] 2.9219220 4.6750752 -9.3501504 1.7531532 1.7531532 0.5843844
## [4,] 0.0000000 -0.5843844 1.7531532 -9.3501504 -8.1813816 0.0000000
## [5,] -1.1687688 -0.5843844 1.7531532 -8.1813816 -9.3501504 -1.1687688
## [6,] 1.1687688 -2.9219220 0.5843844 0.0000000 -1.1687688 -9.3501504
## [7,] 0.0000000 0.5843844 1.7531532 -7.0126128 -7.0126128 1.1687688
## [,7]
## [1,] 0.0000000
## [2,] 0.5843844
## [3,] 1.7531532
## [4,] -7.0126128
## [5,] -7.0126128
## [6,] 1.1687688
## [7,] -9.3501504(t(W)%*%W)*-0.1815779## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -5.8104928 -0.3631558 1.8157790 0.0000000 -0.7263116 0.7263116
## [2,] -0.3631558 -5.8104928 2.9052464 -0.3631558 -0.3631558 -1.8157790
## [3,] 1.8157790 2.9052464 -5.8104928 1.0894674 1.0894674 0.3631558
## [4,] 0.0000000 -0.3631558 1.0894674 -5.8104928 -5.0841812 0.0000000
## [5,] -0.7263116 -0.3631558 1.0894674 -5.0841812 -5.8104928 -0.7263116
## [6,] 0.7263116 -1.8157790 0.3631558 0.0000000 -0.7263116 -5.8104928
## [7,] 0.0000000 0.3631558 1.0894674 -4.3578696 -4.3578696 0.7263116
## [,7]
## [1,] 0.0000000
## [2,] 0.3631558
## [3,] 1.0894674
## [4,] -4.3578696
## [5,] -4.3578696
## [6,] 0.7263116
## [7,] -5.8104928(t(W)%*%W)*0.1264359## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 4.0459488 0.2528718 -1.2643590 0.0000000 0.5057436 -0.5057436
## [2,] 0.2528718 4.0459488 -2.0229744 0.2528718 0.2528718 1.2643590
## [3,] -1.2643590 -2.0229744 4.0459488 -0.7586154 -0.7586154 -0.2528718
## [4,] 0.0000000 0.2528718 -0.7586154 4.0459488 3.5402052 0.0000000
## [5,] 0.5057436 0.2528718 -0.7586154 3.5402052 4.0459488 0.5057436
## [6,] -0.5057436 1.2643590 -0.2528718 0.0000000 0.5057436 4.0459488
## [7,] 0.0000000 -0.2528718 -0.7586154 3.0344616 3.0344616 -0.5057436
## [,7]
## [1,] 0.0000000
## [2,] -0.2528718
## [3,] -0.7586154
## [4,] 3.0344616
## [5,] 3.0344616
## [6,] -0.5057436
## [7,] 4.0459488(t(W)%*%W)*0.2038857## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 6.5243424 0.4077714 -2.0388570 0.0000000 0.8155428 -0.8155428
## [2,] 0.4077714 6.5243424 -3.2621712 0.4077714 0.4077714 2.0388570
## [3,] -2.0388570 -3.2621712 6.5243424 -1.2233142 -1.2233142 -0.4077714
## [4,] 0.0000000 0.4077714 -1.2233142 6.5243424 5.7087996 0.0000000
## [5,] 0.8155428 0.4077714 -1.2233142 5.7087996 6.5243424 0.8155428
## [6,] -0.8155428 2.0388570 -0.4077714 0.0000000 0.8155428 6.5243424
## [7,] 0.0000000 -0.4077714 -1.2233142 4.8932568 4.8932568 -0.8155428
## [,7]
## [1,] 0.0000000
## [2,] -0.4077714
## [3,] -1.2233142
## [4,] 4.8932568
## [5,] 4.8932568
## [6,] -0.8155428
## [7,] 6.5243424(t(W)%*%W)*0.2152630## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 6.888416 0.430526 -2.152630 0.000000 0.861052 -0.861052 0.000000
## [2,] 0.430526 6.888416 -3.444208 0.430526 0.430526 2.152630 -0.430526
## [3,] -2.152630 -3.444208 6.888416 -1.291578 -1.291578 -0.430526 -1.291578
## [4,] 0.000000 0.430526 -1.291578 6.888416 6.027364 0.000000 5.166312
## [5,] 0.861052 0.430526 -1.291578 6.027364 6.888416 0.861052 5.166312
## [6,] -0.861052 2.152630 -0.430526 0.000000 0.861052 6.888416 -0.861052
## [7,] 0.000000 -0.430526 -1.291578 5.166312 5.166312 -0.861052 6.888416(t(W)%*%W)*-0.4820450## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] -15.42544 -0.96409 4.82045 0.00000 -1.92818 1.92818 0.00000
## [2,] -0.96409 -15.42544 7.71272 -0.96409 -0.96409 -4.82045 0.96409
## [3,] 4.82045 7.71272 -15.42544 2.89227 2.89227 0.96409 2.89227
## [4,] 0.00000 -0.96409 2.89227 -15.42544 -13.49726 0.00000 -11.56908
## [5,] -1.92818 -0.96409 2.89227 -13.49726 -15.42544 -1.92818 -11.56908
## [6,] 1.92818 -4.82045 0.96409 0.00000 -1.92818 -15.42544 1.92818
## [7,] 0.00000 0.96409 2.89227 -11.56908 -11.56908 1.92818 -15.42544(t(W)%*%W)*-0.2153164## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -6.8901248 -0.4306328 2.1531640 0.0000000 -0.8612656 0.8612656
## [2,] -0.4306328 -6.8901248 3.4450624 -0.4306328 -0.4306328 -2.1531640
## [3,] 2.1531640 3.4450624 -6.8901248 1.2918984 1.2918984 0.4306328
## [4,] 0.0000000 -0.4306328 1.2918984 -6.8901248 -6.0288592 0.0000000
## [5,] -0.8612656 -0.4306328 1.2918984 -6.0288592 -6.8901248 -0.8612656
## [6,] 0.8612656 -2.1531640 0.4306328 0.0000000 -0.8612656 -6.8901248
## [7,] 0.0000000 0.4306328 1.2918984 -5.1675936 -5.1675936 0.8612656
## [,7]
## [1,] 0.0000000
## [2,] 0.4306328
## [3,] 1.2918984
## [4,] -5.1675936
## [5,] -5.1675936
## [6,] 0.8612656
## [7,] -6.8901248(t(W)%*%W)*0.1177636## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 3.7684352 0.2355272 -1.1776360 0.0000000 0.4710544 -0.4710544
## [2,] 0.2355272 3.7684352 -1.8842176 0.2355272 0.2355272 1.1776360
## [3,] -1.1776360 -1.8842176 3.7684352 -0.7065816 -0.7065816 -0.2355272
## [4,] 0.0000000 0.2355272 -0.7065816 3.7684352 3.2973808 0.0000000
## [5,] 0.4710544 0.2355272 -0.7065816 3.2973808 3.7684352 0.4710544
## [6,] -0.4710544 1.1776360 -0.2355272 0.0000000 0.4710544 3.7684352
## [7,] 0.0000000 -0.2355272 -0.7065816 2.8263264 2.8263264 -0.4710544
## [,7]
## [1,] 0.0000000
## [2,] -0.2355272
## [3,] -0.7065816
## [4,] 2.8263264
## [5,] 2.8263264
## [6,] -0.4710544
## [7,] 3.7684352(t(W)%*%W)*0.7768588## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 24.859482 1.553718 -7.768588 0.000000 3.107435 -3.107435 0.000000
## [2,] 1.553718 24.859482 -12.429741 1.553718 1.553718 7.768588 -1.553718
## [3,] -7.768588 -12.429741 24.859482 -4.661153 -4.661153 -1.553718 -4.661153
## [4,] 0.000000 1.553718 -4.661153 24.859482 21.752046 0.000000 18.644611
## [5,] 3.107435 1.553718 -4.661153 21.752046 24.859482 3.107435 18.644611
## [6,] -3.107435 7.768588 -1.553718 0.000000 3.107435 24.859482 -3.107435
## [7,] 0.000000 -1.553718 -4.661153 18.644611 18.644611 -3.107435 24.859482(t(W)%*%W)*0.14293337## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 4.5738678 0.2858667 -1.4293337 0.0000000 0.5717335 -0.5717335
## [2,] 0.2858667 4.5738678 -2.2869339 0.2858667 0.2858667 1.4293337
## [3,] -1.4293337 -2.2869339 4.5738678 -0.8576002 -0.8576002 -0.2858667
## [4,] 0.0000000 0.2858667 -0.8576002 4.5738678 4.0021344 0.0000000
## [5,] 0.5717335 0.2858667 -0.8576002 4.0021344 4.5738678 0.5717335
## [6,] -0.5717335 1.4293337 -0.2858667 0.0000000 0.5717335 4.5738678
## [7,] 0.0000000 -0.2858667 -0.8576002 3.4304009 3.4304009 -0.5717335
## [,7]
## [1,] 0.0000000
## [2,] -0.2858667
## [3,] -0.8576002
## [4,] 3.4304009
## [5,] 3.4304009
## [6,] -0.5717335
## [7,] 4.5738678(t(W)%*%W)*-0.01481522## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -0.47408704 -0.02963044 0.14815220 0.00000000 -0.05926088 0.05926088
## [2,] -0.02963044 -0.47408704 0.23704352 -0.02963044 -0.02963044 -0.14815220
## [3,] 0.14815220 0.23704352 -0.47408704 0.08889132 0.08889132 0.02963044
## [4,] 0.00000000 -0.02963044 0.08889132 -0.47408704 -0.41482616 0.00000000
## [5,] -0.05926088 -0.02963044 0.08889132 -0.41482616 -0.47408704 -0.05926088
## [6,] 0.05926088 -0.14815220 0.02963044 0.00000000 -0.05926088 -0.47408704
## [7,] 0.00000000 0.02963044 0.08889132 -0.35556528 -0.35556528 0.05926088
## [,7]
## [1,] 0.00000000
## [2,] 0.02963044
## [3,] 0.08889132
## [4,] -0.35556528
## [5,] -0.35556528
## [6,] 0.05926088
## [7,] -0.47408704(t(W)%*%W)*0.05403386## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 1.7290835 0.1080677 -0.5403386 0.0000000 0.2161354 -0.2161354
## [2,] 0.1080677 1.7290835 -0.8645418 0.1080677 0.1080677 0.5403386
## [3,] -0.5403386 -0.8645418 1.7290835 -0.3242032 -0.3242032 -0.1080677
## [4,] 0.0000000 0.1080677 -0.3242032 1.7290835 1.5129481 0.0000000
## [5,] 0.2161354 0.1080677 -0.3242032 1.5129481 1.7290835 0.2161354
## [6,] -0.2161354 0.5403386 -0.1080677 0.0000000 0.2161354 1.7290835
## [7,] 0.0000000 -0.1080677 -0.3242032 1.2968126 1.2968126 -0.2161354
## [,7]
## [1,] 0.0000000
## [2,] -0.1080677
## [3,] -0.3242032
## [4,] 1.2968126
## [5,] 1.2968126
## [6,] -0.2161354
## [7,] 1.7290835(t(W)%*%W)*0.62533473## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 20.010711 1.250669 -6.253347 0.000000 2.501339 -2.501339 0.000000
## [2,] 1.250669 20.010711 -10.005356 1.250669 1.250669 6.253347 -1.250669
## [3,] -6.253347 -10.005356 20.010711 -3.752008 -3.752008 -1.250669 -3.752008
## [4,] 0.000000 1.250669 -3.752008 20.010711 17.509372 0.000000 15.008034
## [5,] 2.501339 1.250669 -3.752008 17.509372 20.010711 2.501339 15.008034
## [6,] -2.501339 6.253347 -1.250669 0.000000 2.501339 20.010711 -2.501339
## [7,] 0.000000 -1.250669 -3.752008 15.008034 15.008034 -2.501339 20.010711(t(W)%*%W)*-0.73984570## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] -23.675062 -1.479691 7.398457 0.000000 -2.959383 2.959383
## [2,] -1.479691 -23.675062 11.837531 -1.479691 -1.479691 -7.398457
## [3,] 7.398457 11.837531 -23.675062 4.439074 4.439074 1.479691
## [4,] 0.000000 -1.479691 4.439074 -23.675062 -20.715680 0.000000
## [5,] -2.959383 -1.479691 4.439074 -20.715680 -23.675062 -2.959383
## [6,] 2.959383 -7.398457 1.479691 0.000000 -2.959383 -23.675062
## [7,] 0.000000 1.479691 4.439074 -17.756297 -17.756297 2.959383
## [,7]
## [1,] 0.000000
## [2,] 1.479691
## [3,] 4.439074
## [4,] -17.756297
## [5,] -17.756297
## [6,] 2.959383
## [7,] -23.675062(t(W)%*%W)*0.14873288## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 4.7594522 0.2974658 -1.4873288 0.0000000 0.5949315 -0.5949315
## [2,] 0.2974658 4.7594522 -2.3797261 0.2974658 0.2974658 1.4873288
## [3,] -1.4873288 -2.3797261 4.7594522 -0.8923973 -0.8923973 -0.2974658
## [4,] 0.0000000 0.2974658 -0.8923973 4.7594522 4.1645206 0.0000000
## [5,] 0.5949315 0.2974658 -0.8923973 4.1645206 4.7594522 0.5949315
## [6,] -0.5949315 1.4873288 -0.2974658 0.0000000 0.5949315 4.7594522
## [7,] 0.0000000 -0.2974658 -0.8923973 3.5695891 3.5695891 -0.5949315
## [,7]
## [1,] 0.0000000
## [2,] -0.2974658
## [3,] -0.8923973
## [4,] 3.5695891
## [5,] 3.5695891
## [6,] -0.5949315
## [7,] 4.7594522(t(W)%*%W)*0.12607242## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 4.0343174 0.2521448 -1.2607242 0.0000000 0.5042897 -0.5042897
## [2,] 0.2521448 4.0343174 -2.0171587 0.2521448 0.2521448 1.2607242
## [3,] -1.2607242 -2.0171587 4.0343174 -0.7564345 -0.7564345 -0.2521448
## [4,] 0.0000000 0.2521448 -0.7564345 4.0343174 3.5300278 0.0000000
## [5,] 0.5042897 0.2521448 -0.7564345 3.5300278 4.0343174 0.5042897
## [6,] -0.5042897 1.2607242 -0.2521448 0.0000000 0.5042897 4.0343174
## [7,] 0.0000000 -0.2521448 -0.7564345 3.0257381 3.0257381 -0.5042897
## [,7]
## [1,] 0.0000000
## [2,] -0.2521448
## [3,] -0.7564345
## [4,] 3.0257381
## [5,] 3.0257381
## [6,] -0.5042897
## [7,] 4.0343174This is the condition indicies of the WTW matrix, where the biggest eigenvalue is divided by the other eigenvalues. The results show enough difference between the various condition indicies, showing that collinearity is low in these indicies.
85.586727/52.045588## [1] 1.64445785.586727/38.744747## [1] 2.20898985.586727/23.638622## [1] 3.62063185.586727/13.176761## [1] 6.49527885.586727/7.662141## [1] 11.1700885.586727/3.145413## [1] 27.21001Note that the echo = FALSE parameter was added to the
code chunk to prevent printing of the R code that generated the
plot.