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Topic: Correlation matrix

	PA 765: Correlation
		Beside Pearsonian correlation (r), the most common type, there are other special types of correlation to handle the special characteristics of such types of variables as dichotomies, and there are other measures of association for nominal and ordinal variables.
		Tetrachoric correlation is sometimes used in structural equation modeling (SEM) during the data preparation phase of tailoring the input correlation matrix and is computed by PRELIS, companion software to LISREL, a SEM package distributed by Scientific Software International.
		Eta, the coefficient of nonlinear correlation, known as the correlation ratio, is discussed in the section on analysis of variance.
	www2.chass.ncsu.edu /garson/pa765/correl.htm (3727 words)

	Correlation - Wikipedia, the free encyclopedia
		The correlation is 1 in the case of an increasing linear relationship, −1 in the case of a decreasing linear relationship, and some value in between in all other cases, indicating the degree of linear dependence between the variables.
		This is because the interpretation of a correlation coefficient depends on the context and purposes.
		However, correlations are not presumed to be acausal, though the causes may not be known.
	en.wikipedia.org /wiki/Correlation_matrix (1733 words)

	Matrix Algebra
		Elements (entries) of the matrix are referred to by the name of the matrix in lower case with a given row and column (again, row comes first).
		(The main or principal diagonal in matrix B is composed of elements all equal to 1.) With a square, symmetric matrix, the transpose of the matrix is the original matrix.
		Multiplying a matrix by the identity matrix is analogous to the real number operation of multiplying a number or variable by 1: the resulting output is identical to the numbers input.
	luna.cas.usf.edu /~mbrannic/files/regression/matalg.html (1775 words)

	Basic Statistics
		Pearson correlation (hereafter called correlation), assumes that the two variables are measured on at least interval scales (see Elementary Concepts), and it determines the extent to which values of the two variables are "proportional" to each other.
		For example, there is a correlation between the total amount of losses in a fire and the number of firemen that were putting out the fire; however, what this correlation does not indicate is that if you call fewer firemen then you would lower the losses.
		Because the value of the correlation coefficient is not a linear function of the magnitude of the relation between the variables, correlation coefficients cannot simply be averaged.
	www.statsoft.com /textbook/stbasic.html#scoefficient (9424 words)

	Noise Correlation Matrix Transformations
		The noise wave correlation matrix of a passive linear circuit generating thermal noise can simply be calculated using Bosma's theorem.
		The noise wave correlation matrices of active devices can be determined by forming the noise current correlation matrix and then transforming it to the equivalent noise wave correlation matrix.
		Each element in the diagonal matrix is equal to the sum of the noise current of each element connected to the corresponding node.
	qucs.sourceforge.net /tech/node11.html (390 words)

	Covariance and Correlation
		Covariance and correlation are related parameters that indicate the extent to which two random variables co-vary.
		Due to the symmetry property of covariances, this is necessarily a symmetric matrix.
		Cholesky matrix A lower-triangular matrix that acts as a matrix "square root" for a positive definite matrix.
	www.riskglossary.com /articles/correlation.htm (348 words)

	Help ShowCorrelation - Correlation Visualization
		The correlation matrix is symmetric: correlation between x1 and x3 is the same as the correlation between x3 and x1.
		The correlation matrix is (with 0 in the upper diagonals):
		One heuristic method that "preserves the correlation structure" is to multiply all off-diagonal matrix elements by a constant (0.9, 0.8, 0.7...) until the matrix becomes positive definite.
	www.inductive.com /help-doc-correl.htm (1361 words)

	statistiXL: Statistical Power for Microsoft Excel
		Correlation is a measure of the relationship between two variables, or sets of variables.
		The correlation coefficient is a measure of the strength of the correlation; it varies from –1 (perfect inverse correlation) through 0 (no correlation) to +1 (perfect positive correlation).
		The correlation matrix of r values for all combinations of the selected variables is presented, along with a corresponding matrix of P values for each of the r values.
	www.statistixl.com /features/correlation.aspx (373 words)

	Correlation
		Correlation should only be used when there is no clear cut predictor or response variable and you are only interested if there is an apparent linear relationship between the two interval or ratio scaled variables.
		The entries in the matrix are scatterplots for all the pairs of variables.
		The sample correlation coefficient (denoted by the symbol r) by measures the strength of the linear relationship between two interval or ratio variables.
	www.math.sfu.ca /~cschwarz/Stat-301/Handouts/node43.html (875 words)

	The Multitrait-Multimethod Matrix
		The Multitrait-Multimethod Matrix (hereafter labeled MTMM) is an approach to assessing the construct validity of a set of measures in a study.
		The MTMM is simply a matrix or table of correlations arranged to facilitate the interpretation of the assessment of construct validity.
		Essentially, the MTMM is just a correlation matrix between your measures, with one exception -- instead of 1's along the diagonal (as in the typical correlation matrix) we substitute an estimate of the reliability of each measure as the diagonal.
	www.socialresearchmethods.net /kb/mtmmmat.htm (2121 words)

	Correlation Matrix (Site not responding. Last check: 2007-11-05)
		The correlation coefficient is a numerical measure that quantifies the strength of linear relationships.
		GPA, the grade point average, shows a correlation of 0.4365 with HSM, the high school math average.
		GPA is not as strongly correlated with the other variables and shows a correlation of only 0.1145 with SATV.
	v8doc.sas.com /sashtml/insight/chap18/sect2.htm (97 words)

	pmusic (Site not responding. Last check: 2007-11-05)
		is a matrix of eigenvectors spanning the noise subspace (one per column).
		is the column length in the data matrix case, the matrix size in the correlation matrix case, or the window length for signal vectors.
		where N is the dimension of the eigenvectors and vk is the k-th eigenvector of the correlation matrix of the input signal.
	grove.ufl.edu /matlab_help/toolbox/signal/pmusic.html (938 words)

	Annotated SPSS Output: Principal Components Analysis
		If the correlation matrix is used, the variables are standardized and the total variance will equal the number of variables used in the analysis (because each standardized variable has a variance equal to 1).
		An identity matrix is matrix in which all of the diagonal elements are 1 and all off diagonal elements are 0.
		If the reproduced matrix is very similar to the original correlation matrix, then you know that the components that were extracted accounted for a great deal of the variance in the original correlation matrix, and these few components do a good job of representing the original data.
	www.ats.ucla.edu /STAT/SPSS/output/principal_components.htm (1977 words)

	Correlation Coefficient Testing
		The following JavaScript tests a claimed on a the population's correlation coefficient value based on a set of random paired-observations.
		Enter your up-to-42 sample paired-data set, and the given claimed value for the correlation coefficient by the null hypothesis, then click on the Test button.
		In entering your data to move from cell to cell in the data-matrix use the Tab key not arrow or enter keys.
	home.ubalt.edu /ntsbarsh/Business-stat/otherapplets/correlation.htm (444 words)

	Canonical Analysis
		Therefore, as an overall index of the canonical correlation between two sets of variables, it is customary to report the largest correlation, that is, the one for the first root.
		The tests of significance of the canonical correlations is based on the assumption that the distributions of the variables in the population (from which the sample was drawn) are multivariate normal.
		When there are perfect correlations in the correlation matrix, or if any of the multiple correlations between one variable and the others is perfect (R = 1.0), then the correlation matrix cannot be inverted, and the computations for the canonical analysis cannot be performed.
	www.statsoft.com /textbook/stcanan.html (2846 words)

	The Inverted Correlation Matrix
		The determinant of the correlation matrix will equal 1.0 only if all correlations equal 0, otherwise the determinant will be less than 1.
		Remember that the determinant is related to the volume of the space occupied by the swarm of data points represen ted by standard scores on the measures involved.
		The cofactor matrix is calculated by replacing each element in the matrix with the determinant of what is left after removing both the row and column that the element occupies.
	www.tulane.edu /~PsycStat/dunlap/Psyc613/RI2.html (494 words)

	Correlation Matrix (Site not responding. Last check: 2007-11-05)
		Correlation measures the strength of the linear relationship between two variables.
		A correlation of 0 means that there is no linear association between two variables.
		A correlation of 1 (-1) means that there is an exact positive (negative) linear association between the two variables.
	v8doc.sas.com /sashtml/insight/chap40/sect19.htm (73 words)

	summary
		For the needs of the study, Pearson correlation coefficients were calculated for the linkage between support for the different political parties and turnout on the one hand, and the presence of former State Farms in electoral districts on the other.
		Also noticeable is a positive correlation between pairs of groupings making up different options, as well as between habitation of areas in which State Farms formerly operated and greater support for the left-of-centre option (and to some extent also the component groupings thereof).
		In addition, there was a moderately-strong correlation between the variable of turnout and the presence of State Farms (-0.482), a weak negative correlation between turnout and support for the left-of-centre option (-0.379) and a weak positive correlation between turnout and the right-of-centre option (+0.359).
	www.igipz.pan.pl /miasto/sleszynski/publikacje/2000_slupsk/slupsk_en.htm (3120 words)

	Correlation Matrix Tool - Printer-friendly version of One-Minute Spotlight
		Correlation can increase the accuracy of your simulation's forecast results because you are taking into account the relationships among the uncertain variables.
		Placing the matrix in view on the same sheet lets you view and change the correlations whenever you want.
		The Correlation Matrix tool has quickly imported all of your correlations so that you can spend more of your time running and analyzing simulations.
	www.decisioneering.com /spotlight/printer_friendly/spotlight09_print.html (511 words)

	[No title]
		The correlation is not changed, since it is a linear transformation.
		It is again reasonable, since the matrix used is correlation matrix, which should be the same with or without standardization.
		Within each group, if the matirx used is correlation matrix, or standardization is applied, then the result is the same.
	www.science.gmu.edu /~yxing/igarss (723 words)

	Inverse Correlation Matrix (Site not responding. Last check: 2007-11-05)
		The diagonal elements of the inverse correlation matrix, sometimes referred to as variance inflation factors, measure the extent to which the variables are linear combinations of other variables.
		The jth diagonal element of the inverse correlation matrix is 1/(1 - R
		When a correlation matrix is singular (less than full rank), some variables are linear functions of other variables, and a g2 inverse for the matrix is displayed.
	www.uc.edu /sashtml/insight/chap40/sect21.htm (165 words)

	Correlation
		In every correlation matrix there are two triangles that are the values below and to the left of the diagonal (lower triangle) and above and to the right of the diagonal (upper triangle).
		There is no reason to print both triangles because the two triangles of a correlation matrix are always mirror images of each other (the correlation of variable x with variable y is always equal to the correlation of variable y with variable x).
		For instance, to find the correlation between variables C5 and C2, I look for where row C2 and column C5 is (in this case it's blank because it falls in the upper triangle area) and where row C5 and column C2 is and, in the second case, I find that the correlation is -.166.
	www.socialresearchmethods.net /kb/statcorr.htm (1466 words)

	MMU - Biol. Sci., MSc Multivariate Statistics: Background to eigen analysis (Site not responding. Last check: 2007-11-05)
		Note that a variable correlated with itself always has a correlation coefficient of 1.00, and that the correlation of x with y is the same as that for y with x.
		Thus, for the first matrix they are 1 and 1, for the second 1.25 and 0.75, etc. Note that the eigen values sum to 2, which is the number of variables.
		Matrix 4 has one dimension that is much longer than the other two, that share the same value.
	obelia.jde.aca.mmu.ac.uk /multivar/eigen.htm (1306 words)

	Correlation Matrix (Site not responding. Last check: 2007-11-05)
		The first thing we're struck by is that all the correlations are positive, indicating that rare features stay rare and common features stay common, which is very pointedly NOT how one defines a truly "volatile" space.
		In a truly volatile space, where features appear and disappear unpredictably, these numbers should fluctuate around 0, and about half of them ought to be negative, by sheer luck.
		Far from being rapid, the correlations in each column exhibit a gradual, persistent downward trend.
	www.qaqd.com /research/mit5.htm (265 words)

	Wilmott Forums - Cholesky Factorisation
		Then, either the fourth will be the proximity of the correlated component to the uncorrelated components, like does it sit an equal distance between them, and rain on them both equally, or does it hit one more than the other.
		Therefore, if you create a matrix for whatever purposes (stress testing, maybe), and it has a negative eigenvalue, then it cannot be a true correlation matrix.
		There is no such thing as an exact correlation matrix and the matrix you use will be highly dependent upon sampling periods, frequency etc. At the end of the day you have to price with the correlation that you are most happy with.
	www.wilmott.com /messageview.cfm?catid=3&threadid=2346 (1640 words)

	Myers-Briggs Type Indicator - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-05)
		present correlations between the MBTI scales and the Big Five personality construct, which is a conglomeration of characteristics found in nearly all personality and psychological tests.
		The closer the number is to 1.0 or -1.0, the higher the degree of correlation.
		These correlations show that E-I and S-N are strongly related to extraversion and openness respectively.
	en.wikipedia.org /wiki/Myers_briggs (3725 words)

	Partial Correlation
		The Pearson partial correlation between two variables, after controlling for variables in the PARTIAL statement, is equivalent to the Pearson correlation between the residuals of the two variables after regression on the controlling variables.
		To derive the corresponding Spearman partial rank-order correlations and Kendall partial tau-b correlations, PROC CORR applies the Cholesky decomposition algorithm to the Spearman rank-order correlation matrix and Kendall's tau-b correlation matrix and uses the correlation formula.
		That is, the Spearman partial correlation is equivalent to the Pearson correlation between the residuals of the linear regression of the ranks of the two variables on the ranks of the partialled variables.
	support.sas.com /91doc/getDoc/procstat.hlp/corr_sect16.htm (680 words)

	Systat Software Inc. - Systat - Product Uses
		4) The sum of the squares of the columns of the factor score matrix is the inverse of the eigenvalue corresponding to that column.
		But, in fact, the columns of component loadings are the eigenvectors of the correlation matrix multiplied by the square roots of the eigenvalues of the matrix.
		Note that the eigenvalues for the correlation matrix are identical to those reported in the Factor Analysis output, but the eigenvectors are not the same as the component loadings.
	www.systat.com /products/Systat?sec=1023 (1142 words)

	Analysis Ch5 pg2 ex2 Correlation Matrix (Site not responding. Last check: 2007-11-05)
		Try the following exercise to create a correlation matrix using the variables: WAZ score, education (dummy for low education), housing (dummy for bad roof), sanitation (dummy for no toilet access), water source (dummies for piped, well and river water), and income (virtual variable for income).
		The Pearson's correlation coefficient measures for a linear relationship between the variables of interest and it shows positive or negative direction.
		It is clear that there are strong correlations between the variables of interest and the outcome variable (waz score) for all but pump/tap water.
	www.tulane.edu /~panda2/Analysis2/Multi-way/correlation.htm (290 words)

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