# correlation

## Definitions

• WordNet 3.6
• n correlation a statistical relation between two or more variables such that systematic changes in the value of one variable are accompanied by systematic changes in the other
• n correlation a statistic representing how closely two variables co-vary; it can vary from -1 (perfect negative correlation) through 0 (no correlation) to +1 (perfect positive correlation) "what is the correlation between those two variables?"
• n correlation a reciprocal relation between two or more things
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Webster's Revised Unabridged Dictionary
• Correlation (Physics) etc. Physics See under Accumulation Conservation Correlation, etc.
• n Correlation Reciprocal relation; corresponding similarity or parallelism of relation or law; capacity of being converted into, or of giving place to, one another, under certain conditions; as, the correlation of forces, or of zymotic diseases.
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Century Dictionary and Cyclopedia
• n correlation Reciprocal relation; interdependence or interconnection.
• n correlation The act of bringing into orderly connection or reciprocal relation.
• n correlation In physiology, specifically, the interdependence of organs or functions; the reciprocal relations of organs.
• n correlation In geometry, such a relation between two planes that to each intersection of lines in either there corresponds in the other a line of junction between points corresponding to the intersecting lines in the first plane; also, a relation between two spaces such that to every point in either there corresponds a plane in the other, three planes in either intersecting in a point corresponding to the plane of the three points in the other space to which the three intersecting planes correspond; more generally, a relation between figures, propositions, etc., derivable from one another in an n-dimensional space by interchanging points with (n—1) -dimensional flats.
• n correlation In statistics, the relation of two or more variable quantities. One variable quantity never determines another completely. For instance, in a certain biological type size never completely determines weight, although large individuals are, on the whole, heavy. The values of one variable, which are correlated with a certain value of another variable, are called an array. When the variability is normal, the average deviation of the array is equal to the deviation of the correlated measure multiplied by a constant which is called the coefficient of regression. A comparison of the coefficients of regression of the first variable considered as a series of arrays of the second, and of the second considered as a series of arrays of the first, leads to their reduction to a common coefficient of correlation which equals the average of the products of all the correlated pairs of deviations, divided by the product of their standard or mean square variabilities. The variabilities of the arrays are equal to the variability of each complete series multiplied by √— r where r is the coefficient of correlation.
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## Etymology

Webster's Revised Unabridged Dictionary
LL. correlatio,; L. cor-, + relatio,: cf. F. corrélation,. Cf. Correlation

## Usage

### In literature:

I stay to correlate what goes on outside with what goes on inside.
"Breaking Point" by James E. Gunn
The successive changes of temperament and taste which we mark at home have no correlatives abroad.
"Cornelius O'Dowd Upon Men And Women And Other Things In General Originally Published In Blackwood's Magazine - 1864" by Charles Lever
These two principles were correlative.
"The Oriental Religions in Roman Paganism" by Franz Cumont
Even a recognition that every right has a correlative duty will not meet the needs of democracy.
"The Menorah Journal, Volume 1, 1915" by Various
Certain important correlations, furthermore, have been found between the level of intelligence and the level of character.
"Human Traits and their Social Significance" by Irwin Edman
Such a correlation I am now about to point out.
"Contributions to the Theory of Natural Selection" by Alfred Russel Wallace
Brief mention is also made of correlative variations observed in man.
"Evolution in Modern Thought" by Ernst Haeckel
Was there some correlation between property-holdings, or national origin, and leadership?
"The Fair Play Settlers of the West Branch Valley, 1769-1784" by George D. Wolf
I shall attempt not much of correlation of dates.
"The Book of the Damned" by Charles Fort
Place correlatives so that there can be no doubt as to their office.
"Practical Grammar and Composition" by Thomas Wood
So far we have only a superficial perception of this correlation.
"Researches on Cellulose" by C. F. Cross
Correlative: of a correlated nature; see correlated.
"Explanation of Terms Used in Entomology" by John. B. Smith
This led to the view that holiness and love are, if not identical, at least correlated expressions.
"Holy in Christ" by Andrew Murray
The life of Victor Stott was cut into two distinct sections, between which there is no correlation.
"The Wonder" by J. D. Beresford
But these correlations rest upon imperfect evidence.
"Encyclopaedia Britannica, 11th Edition, Volume 3, Part 1, Slice 3" by Various
Here was the correlated movement.
"The Meaning of Evolution" by Samuel Christian Schmucker
A correlation center tested it, matching it with electrical and chemical data in its memory files.
"Watchbird" by Robert Sheckley
Correlation relates kindred topics of different subjects, while comparison points out relations in the same subject.
"College Teaching" by Paul Klapper
He was striving to correlate all this when made aware that the taxi had stopped and that they were at their destination.
"Mixed Faces" by Roy Norton
But when we correlate brain weight and intelligence in human individuals.
"Psychology" by Robert S. Woodworth
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### In poetry:

In child-way her heart's eye did see
The correlation's node:
"Yes," she said, "God takes care o' me,
An' I take care o' God."
"Reciprocity" by George MacDonald

### In news:

No regional correlations were found between the three PET tracers .
NextBio Clinical Correlates Patient Clinical and Genomic Data to Experimental '-Omics' to Aid Translational Research and Biomarker Discovery.
Which side of the pro-jig/anti-jig movement you fall on has some correlation with where your turf is.
But is there really a direct correlation.
Reducing Operating Costs and Enabling Correlation of Alerts Between Different Analytic Tools.
Students, teachers and support staff at the Jefferson County Vocational School recently attended a bullying prevention program hosted by Don Stanko and Brian Correll of the Digital Innocence Recovery Group from Columbus.
BLOOMINGDALE — Students, teachers and support staff at the Jefferson County Vocational School recently attended a bullying prevention program hosted by Don Stanko and Brian Correll of the Digital.
Printer manufacturers' published speeds are typically "up-to" speeds and do not always correlate to actual production modes.
In 2006, he started a nonprofit for just such a reason and a correlating website, HistoricWoolenMills.org.
The size of the word directly correlates to the amount of times it was mentioned in residents' comments.
The uptake was analyzed to gauge the correlation between the subjects' dopamine synthesis capacity and aggressive behavior.
Our Voice on Oct 31 ("Don't tell anybody, but the Earth's climate is changing") as I see it suggests a correlation between our national energy policy and natural disasters such as Hurricane Sandy.
A recently published French study suggests a horse's neck posture might indicate correlating back pain.
Specifically, we are looking at the behaviors and evidence that are correlated with student performance.
Answering such questions has always been difficult, since correlating current consumption with software code has traditionally been a somewhat inexact and cumbersome task.
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### In science:

III E, random lattices can exhibit long-range correlations, characterized by a correlation length ξ , in local elastic moduli that can significantly modify the behavior of nonaﬃnity correlation functions at distances less than ξ .
Nonaffine Correlations in Random Elastic Media
We calculate the nonaﬃnity displacement correlation function, G (x) = h[u′ (x) − u′ (0)]2 i, and the vorticity correlation function, Gω (x) = hω (x)ω (0)i analytically and verify their form in numerical simulations for systems with both short- and long-range correlations in local elastic moduli.
Nonaffine Correlations in Random Elastic Media
Thus, when correlation times are long, even if hrms is not too large the optimal estimator integrates for a time much shorter than the correlation time—e.g., with correlation times over order 100 events, τint ∼ 10 − 15 events, in reasonable agreement with the results of Ref .
Should you believe that this coin is fair?
Exactly at criticality, the typical and averaged correlations are also very different, since the typical correlation decays as Ctyp (r) ∼ e−w√r , where w is a random variable of order 1, whereas the averaged correlation is dominated by rare events and decays algebraically C (r) ∼ 1/r(3−√5)/2 .
Random walks and polymers in the presence of quenched disorder
For a data set with n variables, the most basic way to analyze the multidimensional structure of the correlations between all the variables is to organize the linear correlation coefﬁcients R between all possible pairs of variables in matrix form, i.e., to construct a correlation matrix.
Statistical analysis of BATSE gamma-ray bursts: Self-similarity and the Amati-relation
We ﬁnd a weak correlation between F and V , which is probably a consequence of the correlation between F and T50 (as we will show later in § 5.3) and most likely has no relation with the luminosity-variability correlation claimed by Reichart et al. (2001) since for our sample R[log F,log V ] = 0.01.
Statistical analysis of BATSE gamma-ray bursts: Self-similarity and the Amati-relation
The sign of fx (with x = ci, ne, nv) determines the nature of the correlation: a positive correlation (fx > 0) results in extra power to the Sachs–Wolfe plateau, a negative correlation (fx < 0) subtracts power in the region ℓ <∼ 50.
The isocurvature fraction after WMAP 3-year data
Values of rX Y near 0 suggest absence of linear correlation between the two variables, while values around 1 and −1 indicate correlated or anti-correlated behavior, respectively.
Identifying Complex Networks by Random Walks
It is then important to understand whether an effect like clustering, which depends on pair-correlation, is due to the effect of the many weakly correlated particle pairs, or to the one of the few strongly correlated ones.
Concentration fluctuations of large Stokes number particles in a one-dimensional random velocity field
Presented in Figure 11, left to right are (a) eigenvalue distribution of interactions with two temporarily correlated time series, (b) IPR of eigenvectors of interactions with two temporarily correlated time series, (c) the overlap matrix of deviating eigenvectors with two temporarily correlated time series.
Analysis of Inter-Domain Traffic Correlations: Random Matrix Theory Approach
It is also important to note that ﬁnding a good hcp SQS is more diﬃcult than ﬁnding an SQS of cubic structures with the same range of matching correlations due to the fact that, for a given range of correlations, there are more symmetrically distinct correlations to match.
Thermodynamic properties of binary HCP solution phases from special quasirandom structures
The auto-correlation and cross-correlation of the symbolic sequence { }ns are also given in Fig8(a,b). It can be seen that { }ns has δ-like auto-correlation which is required for a good PRBGs.
Pseudo-random number generator based on asymptotic deterministic randomness
We considered three possible combinations of data: Planck alone, Planck plus its cross-correlation with DES or LSST (but no information on galaxy auto-correlations), and ﬁnally Planck plus LSST, using all information and including the correlation.
Constraining neutrino masses with the ISW-galaxy correlation function
The transition between both limits is governed by the correlation of the distances di j and d j i : for positive correlations the AP problem is in the “SM regime ”, whereas for anti correlated distances it is “near ” the TSP regime.
On the number of \$k\$-cycles in the assignment problem for random matrices
INTRODUCT ION What is the intrinsic connection between correlated random variables? How much interaction is necessary to create correlation? Many fruitful efforts have been made to quantify correlation between two random variables.
Communication Requirements for Generating Correlated Random Variables
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