
## coda analysis
student<-read.coda('coda-uniform.txt','index-uniform.txt')
geweke.diag(student,.2,.5)
HPDinterval(student)

## history plot
## plot coda
coda<-read.table('/Volumes/~zzhang4/Private/zzy/research/Bayesian analysis of longitudinal data/Student t distribution/real-data-analysis/latent basis coda chain.txt')

par<-matrix(c(coda[,2]),ncol=11)

## history plot
par(mfrow=c(5,2), mar=c(3, 5, 1, 1) + 0.1)

plot.ts(par[,1], ylab='A[2]')
plot.ts(par[,2], ylab='A[3]')
plot.ts(par[,3], ylab='A[4]')
plot.ts(par[,9], ylab=quote(beta[L]))
plot.ts(par[,10], ylab=quote(beta[S]))
plot.ts(par[,4], ylab=quote(sigma[L]^2))
plot.ts(par[,5], ylab=quote(sigma[S]^2))
plot.ts(par[,6], ylab=quote(sigma[LS]))
plot.ts(par[,8], ylab=quote(phi))
plot.ts(par[,11], ylab=quote(k))

normal<-read.coda('coda-norm.txt','index-norm.txt')
geweke.diag(normal, .2,.5)
HPDinterval(normal)

id<-rep(1:7, each=38001)
x<-rep(2000:40000, 7)

par(mfrow=c(7,1), mar=c(3, 5, 1, 1) + 0.1)
plot(x[id==6],  normal[id==6], type='l', ylab=quote(beta[L]), xlab='')
plot(x[id==7],  normal[id==7], type='l', ylab=quote(beta[S]), xlab='')
plot(x[id==1],  normal[id==1], type='l', ylab=quote(sigma[L]^2), xlab='')
plot(x[id==4],  normal[id==4], type='l', ylab=quote(sigma[S]^2), xlab='')
plot(x[id==2],  normal[id==2], type='l', ylab=quote(sigma[LS]), xlab='')
plot(x[id==5],  normal[id==5], type='l', ylab=quote(phi), xlab='')

#####################
## Boxplots

y = matrix( c(
NA, 65.0,  50.0,  61.0,  NA, 
48.0,  44.0,  50.0,  NA, 62.0,  
60.0,  37.0,  42.0,  52.0,  53.0,  
61.0,  85.0,  69.0,  71.0,  71.0,  
NA, 38.0,  72.0,  69.0,  76.0,  
59.0,  79.0,  61.0,  57.0,  70.0,  
52.0,  72.0,  79.0,  69.0,  NA, 
73.0,  79.0,  82.0,  73.0,  90.0,  
41.0,  67.0,  NA, NA, 70.0,  
69.0,  78.0,  72.0,  70.0,  74.0,  
51.0,  45.0,  50.0,  70.0,  69.0,  
63.0,  72.0,  69.0,  74.0,  NA, 
80.0,  85.0,  89.0,  92.0,  97.0,  
78.0,  81.0,  96.0,  97.0,  81.0,  
74.0,  50.0,  NA, 62.0,  38.0,  
80.0,  65.0,  85.0,  86.0,  86.0,  
63.0,  72.0,  64.0,  NA, 69.0,  
68.0,  86.0,  73.0,  90.0,  95.0,  
82.0,  92.0,  95.0,  97.0,  98.0,  
61.0,  58.0,  79.0,  72.0,  72.0,  
76.0,  55.0,  69.0,  82.0,  58.0,  
80.0,  81.0,  87.0,  85.0,  92.0,  
50.0,  48.0,  61.0,  73.0,  50.0,  
64.0,  NA, 57.0,  65.0,  55.0,  
93.0,  93.0,  95.0,  97.0,  100.0,  
50.0,  58.0,  77.0,  76.0,  58.0,  
49.0,  54.0,  72.0,  65.0,  64.0,  
58.0,  62.0,  81.0,  81.0,  84.0,  
60.0,  70.0,  72.0,  82.0,  83.0,  
67.0,  90.0,  84.0,  72.0,  87.0,  
68.0,  80.0,  85.0,  90.0,  89.0,  
66.0,  59.0,  60.0,  70.0,  71.0,  
75.0,  76.0,  81.0,  85.0,  79.0,  
90.0,  89.0,  97.0,  95.0,  100.0,  
73.0,  76.0,  81.0,  79.0,  85.0,  
44.0,  50.0,  NA, 55.0,  53.0,  
31.0,  NA, 28.0,  NA, NA, 
60.0,  56.0,  67.0,  65.0,  72.0,  
79.0,  68.0,  98.0,  88.0,  73.0,  
92.0,  80.0,  91.0,  NA, 78.0,  
35.0,  62.0,  70.0,  74.0,  74.0,  
39.0,  50.0,  71.0,  NA, 75.0,  
61.0,  88.0,  63.0,  83.0,  79.0,  
70.0,  63.0,  64.0,  70.0,  91.0,  
69.0,  53.0,  65.0,  66.0,  NA, 
60.0,  67.0,  75.0,  70.0,  80.0,  
24.0,  48.0,  42.0,  52.0,  59.0,  
40.0,  50.0,  66.0,  67.0,  59.0,  
NA, 29.0,  49.0,  49.0,  45.0,  
55.0,  63.0,  79.0,  69.0,  68.0,  
60.0,  47.0,  52.0,  49.0,  NA, 
54.0,  64.0,  78.0,  68.0,  71.0,  
61.0,  75.0,  77.0,  93.0,  NA, 
58.0,  47.0,  61.0,  50.0,  53.0,  
40.0,  56.0,  51.0,  62.0,  57.0,  
85.0,  74.0,  100.0,  92.0,  95.0,  
60.0,  57.0,  83.0,  77.0,  82.0,  
58.0,  NA, 49.0,  55.0,  80.0,  
60.0,  88.0,  89.0,  89.0,  NA, 
75.0,  73.0,  74.0,  82.0,  89.0,  
54.0,  45.0,  43.0,  57.0,  50.0,  
44.0,  NA, 46.0,  73.0,  73.0,  
30.0,  57.0,  30.0,  59.0,  40.0,  
70.0,  NA, 94.0,  NA, 97.0,  
51.0,  59.0,  49.0,  25.0,  61.0,  
84.0,  89.0,  95.0,  93.0,  95.0,  
58.0,  67.0,  NA, 83.0,  83.0,  
61.0,  60.0,  65.0,  89.0,  91.0,  
56.0,  51.0,  61.0,  60.0,  55.0,  
65.0,  68.0,  72.0,  66.0,  62.0,  
66.0,  73.0,  NA, 69.0,  NA, 
58.0,  58.0,  60.0,  74.0,  74.0,  
39.0,  53.0,  NA, NA, 65.0,  
59.0,  76.0,  50.0,  NA, 59.0,  
60.0,  NA, 60.0,  NA, 57.0,  
62.0,  74.0,  72.0,  NA, 68.0,  
NA, 66.0,  49.0,  66.0,  NA, 
85.0,  88.0,  91.0,  97.0,  96.0,  
58.0,  49.0,  54.0,  39.0,  50.0,  
50.0,  62.0,  50.0,  74.0,  64.0,  
78.0,  93.0,  NA, 93.0,  92.0,  
58.0,  75.0,  61.0,  52.0,  68.0,  
63.0,  59.0,  83.0,  67.0,  59.0,  
67.0,  83.0,  90.0,  92.0,  93.0,  
79.0,  78.0,  86.0,  94.0,  96.0,  
49.0,  58.0,  66.0,  56.0,  68.0,  
50.0,  70.0,  64.0,  68.0,  74.0,  
48.0,  60.0,  56.0,  52.0,  55.0,  
67.0,  74.0,  NA, NA, NA, 
95.0,  96.0,  95.0,  99.0,  98.0,  
NA, 86.0,  88.0,  93.0,  NA, 
66.0,  71.0,  72.0,  NA, NA, 
74.0,  NA, 88.0,  89.0,  NA, 
55.0,  42.0,  27.0,  41.0,  57.0,  
63.0,  50.0,  52.0,  69.0,  67.0,  
NA, 59.0,  75.0,  65.0,  62.0,  
76.0,  83.0,  80.0,  86.0,  77.0,  
67.0,  64.0,  63.0,  92.0,  72.0,  
69.0,  70.0,  73.0,  76.0,  71.0,  
56.0,  NA, 43.0,  68.0,  80.0,  
71.0,  55.0,  72.0,  66.0,  68.0,  
60.0,  37.0,  88.0,  78.0,  85.0,  
69.0,  66.0,  61.0,  73.0,  56.0,  
71.0,  85.0,  74.0,  70.0,  96.0,  
62.0,  65.0,  NA, 22.0,  63.0,  
53.0,  65.0,  67.0,  73.0,  71.0,  
NA, 41.0,  34.0,  NA, 49.0,  
NA, 72.0,  66.0,  73.0,  75.0,  
51.0,  63.0,  60.0,  67.0,  NA, 
56.0,  68.0,  75.0,  NA, 90.0,  
52.0,  62.0,  70.0,  60.0,  71.0,  
16.0,  20.0,  23.0,  26.0,  33.0,  
60.0,  54.0,  62.0,  77.0,  68.0,  
88.0,  96.0,  89.0,  NA, 98.0,  
56.0,  65.0,  75.0,  83.0,  94.0,  
85.0,  89.0,  92.0,  NA, NA, 
66.0,  70.0,  66.0,  69.0,  68.0,  
72.0,  73.0,  74.0,  60.0,  54.0,  
68.0,  82.0,  79.0,  77.0,  91.0,  
60.0,  67.0,  66.0,  81.0,  82.0,  
55.0,  47.0,  34.0,  65.0,  60.0,  
80.0,  90.0,  89.0,  64.0,  88.0,  
67.0,  87.0,  99.0,  87.0,  100.0,  
79.0,  88.0,  73.0,  92.0,  90.0,  
81.0,  78.0,  82.0,  87.0,  89.0,  
65.0,  85.0,  75.0,  88.0,  73.0,  
28.0,  2.0,  54.0,  61.0,  66.0,  
88.0,  87.0,  90.0,  97.0,  96.0,  
75.0,  76.0,  83.0,  87.0,  82.0,  
65.0,  63.0,  69.0,  63.0,  NA, 
75.0,  73.0,  79.0,  81.0,  75.0,  
70.0,  72.0,  85.0,  89.0,  93.0,  
58.0,  46.0,  53.0,  70.0,  67.0,  
83.0,  87.0,  86.0,  97.0,  87.0,  
66.0,  69.0,  68.0,  89.0,  92.0,  
65.0,  59.0,  66.0,  73.0,  NA, 
37.0,  36.0,  NA, 43.0,  45.0,  
78.0,  83.0,  63.0,  74.0,  88.0,  
47.0,  55.0,  58.0,  67.0,  76.0,  
97.0,  50.0,  45.0,  100.0,  NA, 
52.0,  56.0,  56.0,  100.0,  76.0,  
44.0,  23.0,  39.0,  100.0,  56.0,  
46.0,  NA, 49.0,  NA, 56.0,  
55.0,  66.0,  66.0,  68.0,  70.0,  
47.0,  52.0,  63.0,  66.0,  69.0,  
49.0,  63.0,  59.0,  62.0,  62.0,  
52.0,  50.0,  56.0,  62.0,  59.0,  
50.0,  47.0,  54.0,  63.0,  63.0,  
56.0,  69.0,  50.0,  75.0,  68.0,  
73.0,  86.0,  75.0,  75.0,  82.0,  
53.0,  57.0,  56.0,  69.0,  71.0,  
70.0,  72.0,  70.0,  72.0,  72.0,  
57.0,  55.0,  55.0,  53.0,  57.0,  
51.0,  58.0,  64.0,  70.0,  63.0,  
53.0,  57.0,  60.0,  70.0,  71.0,  
50.0,  70.0,  70.0,  72.0,  81.0,  
56.0,  55.0,  65.0,  70.0,  68.0,  
49.0,  47.0,  89.0,  69.0,  69.0,  
65.0,  72.0,  65.0,  76.0,  71.0,  
75.0,  78.0,  92.0,  94.0,  94.0,  
68.0,  71.0,  56.0,  75.0,  67.0,  
55.0,  61.0,  60.0,  64.0,  62.0,  
63.0,  71.0,  66.0,  67.0,  3.0,  
56.0,  50.0,  0.0,  59.0,  82.0,  
62.0,  67.0,  63.0,  57.0,  3.0,  
62.0,  53.0,  73.0,  65.0,  75.0,  
56.0,  53.0,  51.0,  NA, 57.0,  
92.0,  70.0,  71.0,  75.0,  71.0,  
NA, 59.0,  65.0,  64.0,  49.0,  
71.0,  69.0,  69.0,  75.0,  93.0,  
86.0,  82.0,  90.0,  91.0,  94.0,  
86.0,  87.0,  92.0,  94.0,  93.0,  
NA, 36.0,  41.0,  46.0,  NA, 
58.0,  54.0,  65.0,  64.0,  62.0,  
69.0,  71.0,  87.0,  81.0,  94.0,  
84.0,  35.0,  29.0,  26.0,  96.0,  
50.0,  70.0,  68.0,  80.0,  100.0,  
76.0,  59.0,  73.0,  89.0,  NA, 
75.0,  90.0,  92.0,  97.0,  99.0,  
43.0,  43.0,  71.0,  46.0,  44.0,  
40.0,  44.0,  40.0,  40.0,  41.0,  
48.0,  48.0,  80.0,  84.0,  82.0,  
70.0,  73.0,  91.0,  71.0,  NA, 
46.0,  45.0,  49.0,  63.0,  65.0,  
38.0,  58.0,  66.0,  65.0,  62.0,  
49.0,  46.0,  66.0,  65.0,  NA, 
74.0,  NA, 70.0,  85.0,  68.0,  
46.0,  75.0,  78.0,  74.0,  68.0,  
70.0,  71.0,  87.0,  91.0,  90.0,  
65.0,  40.0,  60.0,  70.0,  72.0,  
61.0,  54.0,  56.0,  55.0,  65.0,  
48.0,  43.0,  44.0,  80.0,  61.0,  
35.0,  55.0,  57.0,  34.0,  54.0,  
73.0,  72.0,  84.0,  84.0,  87.0,  
NA, 39.0,  62.0,  33.0,  38.0,  
63.0,  93.0,  81.0,  89.0,  72.0,  
73.0,  79.0,  71.0,  75.0,  92.0,  
63.0,  84.0,  75.0,  64.0,  66.0,  
NA, 66.0,  55.0,  66.0,  50.0,  
66.0,  68.0,  69.0,  68.0,  71.0,  
61.0,  57.0,  38.0,  43.0,  71.0,  
63.0,  53.0,  90.0,  85.0,  87.0,  
NA, 54.0,  NA, 70.0,  51.0,  
66.0,  70.0,  60.0,  69.0,  47.0,  
73.0,  94.0,  92.0,  95.0,  96.0,  
61.0,  50.0,  49.0,  50.0,  NA, 
91.0,  NA, 94.0,  NA, 99.0,  
83.0,  76.0,  72.0,  NA, 76.0,  
51.0,  57.0,  NA, NA, 60.0,  
50.0,  60.0,  63.0,  50.0,  50.0,  
64.0,  75.0,  88.0,  NA, 91.0,  
24.0,  NA, NA, 45.0,  NA, 
NA,  91.0,  93.0,  96.0,  95.0,  
51.0,  49.0,  49.0,  99.0,  72.0,  
62.0,  89.0,  91.0,  90.0,  92.0,  
56.0,  65.0,  69.0,  4.0,  71.0,  
63.0,  60.0,  69.0,  64.0,  68.0,  
49.0,  67.0,  77.0,  90.0,  70.0,  
68.0,  71.0,  71.0,  79.0,  83.0,  
59.0,  68.0,  64.0,  62.0,  63.0,  
55.0,  59.0,  68.0,  71.0,  50.0,  
80.0,  81.0,  76.0,  99.0,  88.0,  
48.0,  46.0,  45.0,  66.0,  61.0,  
60.0,  68.0,  69.0,  70.0,  73.0,  
57.0,  64.0,  68.0,  68.0,  67.0,  
63.0,  73.0,  70.0,  57.0,  63.0,  
51.0,  60.0,  53.0,  51.0,  47.0,  
60.0,  74.0,  69.0,  83.0,  69.0,  
53.0,  58.0,  61.0,  61.0,  63.0,  
60.0,  62.0,  57.0,  60.0,  73.0,  
66.0,  75.0,  75.0,  NA, 73.0,  
53.0,  38.0,  36.0,  NA, 40.0,  
47.0,  37.0,  99.0,  98.0,  71.0,  
60.0,  60.0,  94.0,  NA, 62.0,  
69.0,  NA, 71.0,  87.0,  93.0,  
48.0,  23.0,  26.0,  41.0,  52.0,  
54.0,  38.0,  53.0,  NA, 59.0,  
55.0,  59.0,  57.0,  74.0,  76.0,  
65.0,  80.0,  68.0,  72.0,  83.0,  
38.0,  54.0,  44.0,  52.0,  54.0,  
38.0,  28.0,  54.0,  66.0,  67.0,  
17.0,  40.0,  8.0,  22.0,  25.0,  
25.0,  26.0,  70.0,  18.0,  63.0,  
NA, 73.0,  62.0,  85.0,  63.0,  
48.0,  44.0,  59.0,  53.0,  61.0,  
58.0,  70.0,  69.0,  61.0,  60.0,  
80.0,  88.0,  87.0,  93.0,  93.0,  
64.0,  66.0,  86.0,  86.0,  82.0,  
23.0,  1.0,  NA, 55.0,  52.0,  
65.0,  68.0,  64.0,  69.0,  NA, 
85.0,  73.0,  58.0,  64.0,  60.0,  
55.0,  67.0,  69.0,  77.0,  73.0,  
45.0,  52.0,  56.0,  52.0,  75.0,  
31.0,  19.0,  19.0,  50.0,  28.0,  
20.0,  23.0,  38.0,  38.0,  50.0,  
56.0,  68.0,  72.0,  70.0,  67.0,  
64.0,  78.0,  80.0,  74.0,  NA, 
60.0,  54.0,  66.0,  67.0,  NA, 
44.0,  38.0,  47.0,  65.0,  NA, 
60.0,  61.0,  63.0,  60.0,  68.0,  
54.0,  62.0,  69.0,  51.0,  65.0,  
49.0,  47.0,  68.0,  62.0,  72.0,  
44.0,  49.0,  47.0,  47.0,  52.0,  
63.0,  73.0,  72.0,  88.0,  87.0,  
65.0,  77.0,  93.0,  NA, 71.0,  
92.0,  93.0,  97.0,  97.0,  100.0,  
60.0,  75.0,  83.0,  69.0,  68.0,  
59.0,  68.0,  73.0,  75.0,  81.0,  
83.0,  96.0,  88.0,  93.0,  96.0,  
20.0,  61.0,  58.0,  21.0,  40.0,  
76.0,  81.0,  85.0,  67.0,  69.0,  
73.0,  49.0,  56.0,  42.0,  53.0,  
NA, 46.0,  59.0,  57.0,  NA, 
69.0,  82.0,  NA, 72.0,  71.0,  
65.0,  69.0,  NA, 79.0,  83.0,  
42.0,  44.0,  47.0,  50.0,  59.0,  
61.0,  68.0,  72.0,  73.0,  76.0,  
87.0,  90.0,  92.0,  97.0,  90.0,  
67.0,  74.0,  69.0,  77.0,  95.0,  
90.0,  92.0,  90.0,  91.0,  100.0,  
65.0,  59.0,  51.0,  NA, 72.0,  
NA, 59.0,  61.0,  100.0,  62.0,  
85.0,  90.0,  89.0,  90.0,  88.0,  
70.0,  69.0,  64.0,  78.0,  87.0,  
59.0,  75.0,  69.0,  70.0,  76.0,  
71.0,  65.0,  91.0,  94.0,  NA, 
76.0,  80.0,  73.0,  75.0,  78.0,  
69.0,  NA, 80.0,  71.0,  96.0,  
48.0,  57.0,  60.0,  59.0,  67.0,  
54.0,  41.0,  59.0,  68.0,  38.0,  
58.0,  67.0,  94.0,  95.0,  93.0,  
54.0,  48.0,  58.0,  70.0,  70.0,  
64.0,  54.0,  52.0,  35.0,  51.0,  
53.0,  72.0,  68.0,  66.0,  79.0,  
60.0,  70.0,  67.0,  65.0,  72.0,  
31.0,  NA, 40.0,  46.0,  52.0,  
59.0,  61.0,  69.0,  NA, NA, 
59.0,  50.0,  100.0,  61.0,  97.0,  
67.0,  76.0,  74.0,  75.0,  83.0,  
62.0,  92.0,  NA, NA, 55.0,  
52.0,  66.0,  92.0,  76.0,  64.0,  
42.0,  6.0,  48.0,  75.0,  1.0,  
81.0,  73.0,  NA, NA, 72.0,  
34.0,  36.0,  44.0,  54.0,  40.0,  
66.0,  70.0,  NA, NA, 91.0,  
86.0,  56.0,  70.0,  NA, 46.0,  
66.0,  72.0,  79.0,  NA, 79.0,  
49.0,  73.0,  70.0,  78.0,  68.0,  
62.0,  50.0,  61.0,  81.0,  65.0,  
93.0,  90.0,  97.0,  98.0,  100.0,  
22.0,  20.0,  NA, 27.0,  68.0,  
70.0,  70.0,  79.0,  83.0,  85.0,  
81.0,  NA, NA, 91.0,  92.0,  
58.0,  73.0,  73.0,  97.0,  73.0,  
NA,  5.0,  32.0,  39.0,  44.0,  
95.0,  98.0,  97.0,  97.0,  95.0,  
54.0,  60.0,  60.0,  70.0,  71.0,  
72.0,  70.0,  NA, NA, 72.0,  
NA,  49.0,  61.0,  56.0,  54.0,  
NA,  82.0,  72.0,  95.0,  65.0,  
NA,  71.0,  87.0,  67.0,  76.0,  
68.0,  56.0,  88.0,  80.0,  NA, 
55.0,  88.0,  76.0,  94.0,  89.0,  
78.0,  77.0,  88.0,  88.0,  87.0,  
86.0,  91.0,  91.0,  88.0,  96.0,  
62.0,  69.0,  NA, 49.0,  NA, 
31.0,  45.0,  50.0,  41.0,  58.0,  
46.0,  64.0,  NA, 73.0,  70.0,  
61.0,  67.0,  64.0,  65.0,  58.0,  
59.0,  56.0,  59.0,  75.0,  56.0,  
NA, 66.0,  57.0,  71.0,  NA, 
29.0,  44.0,  44.0,  42.0,  63.0,  
49.0,  52.0,  54.0,  62.0,  59.0,  
43.0,  78.0,  70.0,  90.0,  69.0,  
83.0,  68.0,  76.0,  71.0,  69.0,  
63.0,  65.0,  79.0,  72.0,  65.0,  
55.0,  59.0,  59.0,  58.0,  59.0,  
51.0,  69.0,  52.0,  60.0,  38.0,  
28.0,  61.0,  NA, 59.0,  NA, 
58.0,  56.0,  67.0,  66.0,  67.0,  
54.0,  47.0,  58.0,  59.0,  58.0,  
NA, 40.0,  55.0,  68.0,  70.0,  
46.0,  61.0,  54.0,  70.0,  73.0,  
44.0,  56.0,  66.0,  54.0,  67.0,  
63.0,  69.0,  66.0,  68.0,  71.0,  
46.0,  54.0,  64.0,  49.0,  68.0,  
NA, 69.0,  78.0,  58.0,  64.0,  
NA, 57.0,  60.0,  74.0,  51.0,  
68.0,  37.0,  51.0,  56.0,  56.0,  
74.0,  64.0,  78.0,  80.0,  73.0,  
70.0,  65.0,  65.0,  59.0,  66.0,  
83.0,  73.0,  91.0,  93.0,  92.0,  
74.0,  70.0,  53.0,  64.0,  64.0,  
59.0,  56.0,  80.0,  57.0,  54.0,  
72.0,  NA, NA, 49.0,  50.0,  
78.0,  91.0,  89.0,  87.0,  82.0,  
31.0,  1.0,  47.0,  49.0,  57.0,  
84.0,  77.0,  65.0,  87.0,  64.0,  
63.0,  0.0,  64.0,  71.0,  73.0,  
42.0,  50.0,  57.0,  57.0,  62.0,  
31.0,  37.0,  57.0,  41.0,  39.0,  
54.0,  71.0,  88.0,  88.0,  87.0,  
54.0,  NA, 53.0,  46.0,  71.0,  
60.0,  62.0,  62.0,  61.0,  87.0,  
81.0,  61.0,  72.0,  80.0,  88.0,  
88.0,  90.0,  70.0,  92.0,  93.0,  
24.0,  30.0,  27.0,  27.0,  20.0,  
63.0,  58.0,  64.0,  51.0,  64.0,  
79.0,  80.0,  82.0,  87.0,  86.0,  
46.0,  48.0,  63.0,  68.0,  65.0,  
66.0,  69.0,  76.0,  69.0,  65.0,  
68.0,  69.0,  68.0,  70.0,  87.0,  
59.0,  60.0,  64.0,  61.0,  72.0,  
73.0,  86.0,  88.0,  90.0,  NA, 
69.0,  65.0,  69.0,  74.0,  NA),byrow=T, ncol=5)



## 
library(moments)
apply(y, 2, mean, na.rm=T)
apply(y, 2, sd, na.rm=T)
apply(y, 2, skewness, na.rm=T)
apply(y, 2, kurtosis, na.rm=T)

## 
par(mfrow=c(3,2))
qqnorm(y[,1], main='')
qqline(y[,1])

qqnorm(y[,2], main='')
qqline(y[,2])

qqnorm(y[,3], main='')
qqline(y[,3])

qqnorm(y[,4], main='')
qqline(y[,4])

qqnorm(y[,5], main='')
qqline(y[,5])

## boxplots
par(family='times')
boxplot(y[,1],y[,2],y[,3],y[,4],y[,5], names=c('7','8','9','10','11'), ylab='Math Score', xlab='Grade')

boxplot(rnorm(375, mean(y[,1],na.rm=T), sd(y[,1],na.rm=T)), rnorm(375, mean(y[,2],na.rm=T), sd(y[,2],na.rm=T)),rnorm(375, mean(y[,3],na.rm=T), sd(y[,3],na.rm=T)),rnorm(375, mean(y[,4],na.rm=T), sd(y[,4],na.rm=T)),rnorm(375, mean(y[,5],na.rm=T), sd(y[,5],na.rm=T)),add=T, col='red')