Octave で相関係数行列，分散共分散行列

x = [2, 3, 2, 3, 4, 5, 3, 2, 3, 2, 1];
y = [3, 2, 2, 1, 2, 3, 3, 2, 5, 4, 2];

data = [45.51 43.38 56.91 47.32 55.20;
        56.74 61.85 70.44 57.09 55.59;
        32.62 34.17 47.24 43.64 42.45;
        53.43 59.83 47.97 52.18 46.99;
        37.41 36.15 37.70 26.06 30.12;
        42.85 43.91 44.75 53.73 50.74;
        66.06 52.68 39.87 61.52 68.19;
        62.09 62.36 62.01 62.93 59.58;
        50.81 58.48 40.50 48.10 42.55;
        52.48 47.21 52.61 47.42 48.60];

format short

1.　相関係数および相関係数行列

1.1.　ピアソンの積率相関係数

corr(x, y)

ans = 0.073537

corr(data)

ans =

   1.0000   0.8288   0.3214   0.7860   0.7786
   0.8288   1.0000   0.4560   0.7145   0.5004
   0.3214   0.4560   1.0000   0.4643   0.4156
   0.7860   0.7145   0.4643   1.0000   0.8970
   0.7786   0.5004   0.4156   0.8970   1.0000

corr(data(:, 1:2), data(:, 3:5))

ans =

   0.3214   0.7860   0.7786
   0.4560   0.7145   0.5004

1.2.　スピアマンの順位相関係数

spearman(x, y)

ans = 0.070711

spearman(data)

ans =

   1.0000   0.8424   0.3455   0.8424   0.7939
   0.8424   1.0000   0.4909   0.8182   0.5636
   0.3455   0.4909   1.0000   0.3333   0.4545
   0.8424   0.8182   0.3333   1.0000   0.8303
   0.7939   0.5636   0.4545   0.8303   1.0000

spearman(data(:, 1:2), data(:, 3:5))

ans =

   0.3455   0.8424   0.7939
   0.4909   0.8182   0.5636

1.3.　ケンドールの順位相関係数

kendall(x, y)

ans = 0.070593

kendall(data)

ans =

   1.0000   0.7333   0.2444   0.6889   0.6444
   0.7333   1.0000   0.3333   0.6889   0.3778
   0.2444   0.3333   1.0000   0.2000   0.4222
   0.6889   0.6889   0.2000   1.0000   0.6889
   0.6444   0.3778   0.4222   0.6889   1.0000

kendall(data(:, 1:2), data(:, 3:5))

ans =

   0.2444   0.6889   0.6444
   0.3333   0.6889   0.3778

2.　分散共分散行列

usage:
cov (x)
cov (x, opt)
cov (x, y)
cov (x, y, opt)

opt=0 デフォルト 分散，共分散の正規化に n-1 を使う。opt=1 のとき n を使う。

cov(x, y)

ans = 0.090909

cov(data)

ans =

   111.105    92.086    35.715    87.330    86.519
    92.086   111.114    50.665    79.388    55.607
    35.715    50.665   111.117    51.591    46.188
    87.330    79.388    51.591   111.095    99.670
    86.519    55.607    46.188    99.670   111.136

cov(data(:, 1:2), data(:, 3:5))

ans =

   35.715   87.330   86.519
   50.665   79.388   55.607