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Topic: Covariance

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	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.
		It can be shown that covariance matrices are positive definite or positive semidefinite.
	www.riskglossary.com /articles/correlation.htm (348 words)

	PlanetPhysics: covariance and contravariance (Site not responding. Last check: 2007-10-26)
		In the example of cylindrical coordinates, the radial and z components are the same in covariant and contravariant form, but the covariant component of the differential of angle round the z axis is r2dÎ¸ and its integral depends on the path.
		Homology theory is covariant because (as is very clear in singular homology) its basic construction is to take a topological space X and map things into it (in that case, simplices).
		By considering a coordinate transformation on a manifold as a map from the manifold to itself, the transformation of covariant indices of a tensor are given by a pullback, and the transformation properties of the contravariant indices is given by a pushforward.
	planetphysics.org /encyclopedia/CovarianceAndContravariance.html (1326 words)

	Covariance - Wikipedia, the free encyclopedia
		Intuitively, covariance is the measure of how much two variables vary together (as distinct from variance, which measures how much a single variable varies).
		By contrast, correlation, which depends on the covariance, is a dimensionless measure of linear dependence.
		The covariance is sometimes called a measure of "linear dependence" between the two random variables.
	en.wikipedia.org /wiki/Covariance (387 words)

	XVII. Implied Covariance Matrix
		Similarly, the sling between the predictors is the covariance.
		Covariance of Predictor A with Criterion C. The covariance of A with C follows the same rules as before.
		Covariance of Predictor B with Criterion C. This follows the same procedure as described above.
	www.missouri.edu /~wood/psych431/unstpath/unstpath.4.html (616 words)

	Covariance - GSP (Site not responding. Last check: 2007-10-26)
		Covariance, on the other hand, is a measure of how two data sets vary with respect to each other.
		The contribution to the covariance is the area represented by the rectangle, but what we really are doing is multiplying the x and y deviations from their respected mean.
		Similar to variance, we sum each of the points contributions to the covariance and divide by the number of points to find the total covariance.
	www.mste.uiuc.edu /malcz/Spreads/COVARIANCE-GSP.html (1164 words)

	Covariance - CFO.com (Site not responding. Last check: 2007-10-26)
		A positive covariance means that asset returns move together; a negative covariance means returns vary inversely.
		The problem when applying covariance to investing, critics say, is that people interact less predictably than the theory implies.
		To be sure, the principle of covariance works swimmingly well in physics and insurance, says Nassim Nicholas Taleb, a well-known MPT gadfly and chairman of Empirica LLC, a hedge fund.
	www.cfo.com /printable/article.cfm/3007746 (651 words)

	6.5.4.1. Mean Vector and Covariance Matrix
		The mean vector consists of the means of each variable and the variance-covariance matrix consists of the variances of the variables along the main diagonal and the covariances between each pair of variables in the other matrix positions.
		The mean vector is often referred to as the centroid and the variance-covariance matrix as the dispersion or dispersion matrix.
		Also, the terms variance-covariance matrix and covariance matrix are used interchangeably.
	www.itl.nist.gov /div898/handbook/pmc/section5/pmc541.htm (172 words)

	How to Use Tracing Rules to Express Variance/Covariance Matrices: Unstandardized Coefficients
		Variance/covariance matrices summarize the patterns of variability and covariation between variables in the metric of the observed variables.
		Specifically, the model says that the covariance of variables A and C in the model is a sum of two components:
		The covariance of variables B and C in the model is a sum of two components:
	www.missouri.edu /~wood/psych420/rawpath/rawpath.html (1307 words)

	ancova
		Oversimplifying a bit, the analysis of covariance is like an analysis of variance on the residuals of the values of the dependent variable, after removing the influence of the covariate, rather than on the original values themselves.
		The analysis of covariance is used to test the same hypothesis as the one-way analysis of variance.
		[The covariate (Y variable) is only used to reduce the amount of experimental error.] The hypothesis tested is that the population means for the X values corresponding to levels of the independent variable are equal: that the treatments do not differentially effect the dependent variable symbolized by "X".
	bill.psyc.anderson.edu /exdes/ancova.htm (1026 words)

	Covariance
		If the covariance is zero, then the cases in which the product was positive were offset by those in which it was negative, and there is no linear relationship between the two random variables.
		Negative covariance - indicates that higher than average values of one variable tend to be paired with lower than average values of the other variable.
		Because the number representing covariance depends on the units of the data, it is difficult to compare covariances among data sets having different scales.
	www.netmba.com /statistics/covariance (422 words)

	Covariance and contravariance - Wikipedia, the free encyclopedia
		In common physics usage, the adjective covariant may sometimes be used informally as a synonym for invariant (or equivariant, in mathematicians' terms).
		The key property of the tensor representation is the preservation of invariance in the sense that vector components which transform in a covariant manner (or contravariant manner) are paired with basis vectors that transform in a contravariant manner (or covariant manner), and these operations are inverse to one another according to the transformation rules.
		Also note that the covariant basis vectors are parallel to their respective coordinate lines while the contravariant basis vectors are orthogonal to the directions of the other coordinate lines.
	en.wikipedia.org /wiki/Covariant (2334 words)

	Chapter 13
		In addition the covariate (continuous variable) is a pretest that measures the students knowledge prior to exposure to either the curriculum or the teachers.
		Nevertheless, the inclusion of a covariate will increase the statistical power of tests of condition differences, given a covariate that is reliably related to the dependent variable within levels of the categorical variable.
		Since the covariate and the are not orthogonal the sums of squares are not additive as they were when everything was orthogonal.
	espse.ed.psu.edu /espse/hale/507Mat/Chapt13/Chapt13.html (1966 words)

	Covariance Matrix
		The COV= option must be specified to compute an approximate covariance matrix for the parameter estimates under asymptotic theory for least-squares, maximum-likelihood, or Bayesian estimation, with or without corrections for degrees of freedom as specified by the VARDEF= option.
		In small samples, estimates of the covariance matrix based on asymptotic theory are often too small and should be used with caution.
		For minimization, the covariance matrix should be positive definite; for maximization it should be negative definite.
	www.okstate.edu /sas/v7/sashtml/books/ormp/chap5/sect37.htm (753 words)

	Covariance (Site not responding. Last check: 2007-10-26)
		To say "covariant form of Maxwell's equations" is kind of a strange way to fraise it because the everyday form is actually special relativistically covariant again in the literal sence of the word.
		The generally covariant expressions for the electromagnetic field are the electromagnetic and electromagnetic duel tensors.
		This "frame covariance" just means that they have a particular isomorphism as they are mapped from one frame to another by the same transformation as the differntial form of the coordinates.
	www.physicsforums.com /showthread.php?p=121130 (1718 words)

	Eddy Covariance: Measure water vapor, carbon dioxide, heat flux
		Eddy Covariance: Measure water vapor, carbon dioxide, heat flux
		An Eddy Covariance Station measures CO, water vapor, or heat fluxes using the eddy covariance technique.
		If the system will be solar powered, a 65 watt solar panel is the mimimum required.
	www.campbellsci.com /eddy-covariance (138 words)

	Statistical Review with formula of, and rules for the mean, variance, covariance, correlation coefficient (Site not responding. Last check: 2007-10-26)
		The covariance of a random variable with a constant is zero.
		The additive law of covariance holds that the covariance of a random variable with a sum of random variables is just the sum of the covariances with each of the random variables.
		The covariance of a variable with itself is the variance of the random variable.
	www.kaspercpa.com /statisticalreview.htm (548 words)

	Wikinfo \| Covariance (Site not responding. Last check: 2007-10-26)
		The converse, however, is not true: it is possible that X and Y are not independent, yet their covariance is zero.
		That phrase does not mean the same thing that it means in a more formal linear algebraic setting (see linear dependence), although that meaning is not unrelated.
		Images, some of which are used under the doctrine of Fair use or used with permission, may not be available.
	www.wikinfo.org /wiki.php?title=Covariance (312 words)

	use of covariance - java - GameDev.Net Discussion Forums
		Posted - 3/18/2005 8:10:23 AM As I understand covariance is the ability of overrided class functions to return type that is inherited from the base class.
		I mentioned java in the thread name because java natively supports covariance, opposed to c++ where I read (I could be wrong) that covariance is gained through use of templates.
		I thought covariance is somehow a safe way for super type to dynamically cast to child type, so I can get a pointer to super, and then find out what implementation it is and avoid chain of instanceof checks.
	www.gamedev.net /community/forums/viewreply.asp?ID=1961240 (726 words)

	Covariance -- from Wolfram MathWorld
		Covariance provides a measure of the strength of the correlation between two or more sets of random variates.
		However, if the variables are correlated in some way, then their covariance will be nonzero.
		Note that while statistically independent variables are always uncorrelated, the converse is not necessarily true.
	mathworld.wolfram.com /Covariance.html (154 words)

	Patrick Phillips, Evolution of Covariance Structure (Site not responding. Last check: 2007-10-26)
		Genetic covariance structure is a central element for describing multivariate evolutionary change generated by natural selection and genetic drift.
		The average influence of drift leads to proportionality across all traits as expected by theory (outer ovals represent the covariance pattern in the outbred population and the inner ovals represent the average covariance over a large number of inbred popluations).
		For any single population, however, the pattern of covariance can be widely divergent.
	darkwing.uoregon.edu /~pphil/covariance.html (139 words)

	Covariance
		A positive covariance means that asset returns move together.
		One method of calculating covariance is by looking at return surprises (deviations from expected return) in each scenario.
		Another method is to multiply the correlation between the two variables by the standard deviation of each variable.
	www.investopedia.com /terms/c/covariance.asp (292 words)

	Covariance Method (DSP Blockset) (Site not responding. Last check: 2007-10-26)
		Compute a parametric spectral estimate using the covariance method.
		The Covariance Method block estimates the power spectral density (PSD) of the input using the covariance method.
		To guarantee a nonsingular output, you must set the value of this parameter to be less than the input length.
	www.weizmann.ac.il /matlab/toolbox/dspblks/covariancemethod.html (330 words)

	Covariance and Correlation
		Covariance and correlation are closely related parameters that indicate the extent to which two random variables co-vary.
		If the price of one rises, the price of the other is also likely to rise.
		Lady Tasting Tea is a wonderful, non-technical history of statistics.
	www.ee.byu.edu /class/ee483/classnotes/correlation.html (307 words)

	Indirect Covariance NMR Spectroscopy
		This presentation describes recent advancements in the area of indirect covariance NMR spectroscopy reported in a series of publications.
		The presentation will begin with the identification of two types of artifact responses in the indirect covariance spectra and then introduces the concept of unsymmetrical indirect covariance processing as a means of eliminating these artifacts.
		The unsymmetrical indirect covariance processing software is next used to co-process discretely-acquired HSQC and HMBC experiments to give the long-range carbon-carbon connectivity information equivalent to that of an n,n-ADEQUATE experiment without ever having to acquire these low sensitivity data.
	www.acdlabs.com /publish/publ06/njum_indirect_covariance.html (200 words)

	Covariance (Site not responding. Last check: 2007-10-26)
		An object of type Covariance represents the sums of squares and cross products of a multivariate data set divided by the number of observations.
		An object of type Covariance contains the same attributes as an object of type SSCP.
		Since an object of type Covariance contains the mean values (the centroids), the covariances as well as the number of observations it has all the information necessary to be the subject of all kinds of statistical tests on means and variances.
	www.fon.hum.uva.nl /praat/manual/Covariance.html (88 words)

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