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The covariance matrix of the multivariate sample, defined as
n
====
1 \ _ _
S = - > (X - X) (X - X)'
n / j j
====
j = 1
where X_j is the j-th row of the sample matrix.
Example:
(%i1) load ("descriptive")$
(%i2) s2 : read_matrix (file_search ("wind.data"))$
(%i3) fpprintprec : 7$ /* change precision for pretty output */
(%i4) cov (s2);
[ 17.22191 13.61811 14.37217 19.39624 15.42162 ]
[ ]
[ 13.61811 14.98774 13.30448 15.15834 14.9711 ]
[ ]
(%o4) [ 14.37217 13.30448 15.47573 17.32544 16.18171 ]
[ ]
[ 19.39624 15.15834 17.32544 32.17651 20.44685 ]
[ ]
[ 15.42162 14.9711 16.18171 20.44685 24.42308 ]
See also function cov1.
The covariance matrix of the multivariate sample, defined as
n
====
1 \ _ _
S = --- > (X - X) (X - X)'
1 n-1 / j j
====
j = 1
where X_j is the j-th row of the sample matrix.
Example:
(%i1) load ("descriptive")$
(%i2) s2 : read_matrix (file_search ("wind.data"))$
(%i3) fpprintprec : 7$ /* change precision for pretty output */
(%i4) cov1 (s2);
[ 17.39587 13.75567 14.51734 19.59216 15.5774 ]
[ ]
[ 13.75567 15.13913 13.43887 15.31145 15.12232 ]
[ ]
(%o4) [ 14.51734 13.43887 15.63205 17.50044 16.34516 ]
[ ]
[ 19.59216 15.31145 17.50044 32.50153 20.65338 ]
[ ]
[ 15.5774 15.12232 16.34516 20.65338 24.66977 ]
See also function cov.
Function global_variances returns a list of global variance measures:
trace(S_1),
trace(S_1)/p,
determinant(S_1),
sqrt(determinant(S_1)),
determinant(S_1)^(1/p), (defined in: Peña, D.
(2002) Análisis de datos multivariantes; McGraw-Hill, Madrid.)
determinant(S_1)^(1/(2*p)).
where p is the dimension of the multivariate random variable and
S_1 the covariance matrix returned by cov1.
Example:
(%i1) load ("descriptive")$
(%i2) s2 : read_matrix (file_search ("wind.data"))$
(%i3) global_variances (s2);
(%o3) [105.338342060606, 21.06766841212119, 12874.34690469686,
113.4651792608501, 6.636590811800795, 2.576158149609762]
Function global_variances has an optional logical argument:
global_variances (x, true) tells Maxima that x is the data matrix,
making the same as global_variances(x). On the other hand,
global_variances(x, false) means that x is not the data matrix,
but the covariance matrix, avoiding its recalculation,
(%i1) load ("descriptive")$
(%i2) s2 : read_matrix (file_search ("wind.data"))$
(%i3) s : cov1 (s2)$
(%i4) global_variances (s, false);
(%o4) [105.338342060606, 21.06766841212119, 12874.34690469686,
113.4651792608501, 6.636590811800795, 2.576158149609762]
See also cov and cov1.
The correlation matrix of the multivariate sample.
Example:
(%i1) load ("descriptive")$
(%i2) fpprintprec : 7 $
(%i3) s2 : read_matrix (file_search ("wind.data"))$
(%i4) cor (s2);
[ 1.0 .8476339 .8803515 .8239624 .7519506 ]
[ ]
[ .8476339 1.0 .8735834 .6902622 0.782502 ]
[ ]
(%o4) [ .8803515 .8735834 1.0 .7764065 .8323358 ]
[ ]
[ .8239624 .6902622 .7764065 1.0 .7293848 ]
[ ]
[ .7519506 0.782502 .8323358 .7293848 1.0 ]
Function cor has an optional logical argument: cor(x,true) tells
Maxima that x is the data matrix, making the same as cor(x). On
the other hand, cor(x,false) means that x is not the data matrix,
but the covariance matrix, avoiding its recalculation,
(%i1) load ("descriptive")$
(%i2) fpprintprec : 7 $
(%i3) s2 : read_matrix (file_search ("wind.data"))$
(%i4) s : cov1 (s2)$
(%i5) cor (s, false); /* this is faster */
[ 1.0 .8476339 .8803515 .8239624 .7519506 ]
[ ]
[ .8476339 1.0 .8735834 .6902622 0.782502 ]
[ ]
(%o5) [ .8803515 .8735834 1.0 .7764065 .8323358 ]
[ ]
[ .8239624 .6902622 .7764065 1.0 .7293848 ]
[ ]
[ .7519506 0.782502 .8323358 .7293848 1.0 ]
See also cov and cov1.
Function list_correlations returns a list of correlation measures:
-1 ij
S = (s )
1 i,j = 1,2,...,p
2 1
R = 1 - -------
i ii
s s
ii
being an indicator of the goodness of fit of the linear multivariate regression model on X_i when the rest of variables are used as regressors.
ij
s
r = - ------------
ij.rest / ii jj\ 1/2
|s s |
\ /
Example:
(%i1) load ("descriptive")$
(%i2) s2 : read_matrix (file_search ("wind.data"))$
(%i3) z : list_correlations (s2)$
(%i4) fpprintprec : 5$ /* for pretty output */
(%i5) z[1]; /* precision matrix */
[ .38486 - .13856 - .15626 - .10239 .031179 ]
[ ]
[ - .13856 .34107 - .15233 .038447 - .052842 ]
[ ]
(%o5) [ - .15626 - .15233 .47296 - .024816 - .10054 ]
[ ]
[ - .10239 .038447 - .024816 .10937 - .034033 ]
[ ]
[ .031179 - .052842 - .10054 - .034033 .14834 ]
(%i6) z[2]; /* multiple correlation vector */ (%o6) [.85063, .80634, .86474, .71867, .72675]
(%i7) z[3]; /* partial correlation matrix */
[ - 1.0 .38244 .36627 .49908 - .13049 ]
[ ]
[ .38244 - 1.0 .37927 - .19907 .23492 ]
[ ]
(%o7) [ .36627 .37927 - 1.0 .10911 .37956 ]
[ ]
[ .49908 - .19907 .10911 - 1.0 .26719 ]
[ ]
[ - .13049 .23492 .37956 .26719 - 1.0 ]
Function list_correlations also has an optional logical argument:
list_correlations(x,true) tells Maxima that x is the data matrix,
making the same as list_correlations(x). On the other hand,
list_correlations(x,false) means that x is not the data matrix,
but the covariance matrix, avoiding its recalculation.
See also cov and cov1.
Next: Functions and Variables for statistical graphs, Previous: Functions and Variables for descriptive statistics, Nach oben: Package descriptive [Inhalt][Index]