What is linear correlation
A confirmation that the target blip seen on radarscope or the track plotted on a plotting board is the same aircraft on which information is being received.
in biology, the interdependence of the structure and functions of the cells, tissues, organs, and systems of the body, manifested in the body’s development and in its life activities.
The development and existence of the organism as an integral whole is dependent on correlation. The concept was introduced by G. Cuvier (1800–05); however, since he did not accept the theory of evolution, his idea of correlation had a static character, holding that it was evidence of the permanent coexistence of organs. Evolutionary theory gave correlation a dynamic, historical character: the interconnection of the parts of the body is as much the result of their phylogenic development as of their ontogenic development. The problem of correlation was developed from an evolutionary point of view by A. N. Severtsov, and a more profound understanding of it was offered by I. I. ShmaPgauzen.
Several forms of correlation are distinguished. Genomic correlation is a function of the multiple action of hereditary factors (pleiotropy) and of the action of genes that are more closely interrelated (chromosomal correlation). Morphogenetic correlation is the interdependence among the internal factors of individual development. There may be a connection between two or more morphogenetic processes. Thus, it has been shown that the rudiment of the chordamesoderm becomes the inductor that determines the development of the central nervous system and that the optic cup induces the crystalline lens of the eye. Correlation determines the locus and dimensions of a developing organ. Since morphogenetic processes lead to changes in organic inter-relationships, new morphogenetic correlations develop. Thus, a sequential system of morphogenetic correlations gradually un-folds in the course of individual development, becoming one of the chief factors in ontogeny, maintaining the integrity of the organism throughout its development. The data accumulated by developmental biology have enabled some authors to subdivide these correlations into developmental correlations, which de-pend on the activity of the nervous system; functional (ergontic) correlations; and hormonal correlations. Phylogenetic, or phyletic, correlations—the relational changes of the organs during the course of evolution—were considered by Severtsov to be an independent phenomenon, called coordination.
Shmal’gauzen, 1.1. Osnovy sravnitel’noi anatomii pozvonochnykh. 4th ed. Moscow, 1947.
Shmal’gauzen, 1.1. Organizm, kak tseloe v individual’nom i istoricheskom razvitii. Moscow-Leningrad, 1942.
Severtsov, A. N. Morfologicheskie zakonomernosti evoliutsii. Moscow, 1949. (Sobr. soch.. vol. 5.)
Balinsky, B. I. An Introduction to Embryology. 2nd ed. Philadelphia-London, 1965.
in linguistics, the opposition or convergence of linguistic units according to specific features (on all levels of a linguistic system).
Most well developed is the theory of phonological correlation (a phoneme alternation associated with some morphological difference, or forming correlative series that are in opposition according to some one distinctive feature). The notions distinguished include correlative pair (French ã-a, õ-o, ẽ-e, œ̃-œ ), feature (nasalization in French, labiovelarization in the Shona languages of the Bantu family), series (ã, õ, ẽ, œ̃ ), and bundles (in the Archi language, the six-membered bundle z-s-ts-ts’-t̄s-s̄ ).
in mathematical statistics, a probabilistic or statistical relationship, which, generally speaking, does not have a rigorously functional character. In contrast to a functional relationship, a correlative relationship arises either when one of the
random variables depends not only on a given second variable but also on a number of random factors or when, among the conditions upon which one and the other variable depend, there exist some that are common to both of them. A correlation table provides an example of this type of dependence. From Table 1 it is evident that, on the average, an increase in the height of pine trees is accompanied by an increase in the diameter of their trunks; however, pines of a given height (for example, 23 m) possess a distribution of diameters with a fairly large scatter. If, on the average, 23-m pines are thicker than 22-m ones, this relation may be violated to a noticeable extent for individual pines. The statistical correlation in a finite sample being studied is more interesting when it indicates the existence of a link between the phenomena under investigation that conforms to some rule.
Correlation theory is based on the assumption that the phenomena being studied obey some definite probabilistic laws (see PROBABILITY; PROBABILITY THEORY ). The relationship between two random events is manifested by the conditional probability of one of the events, given that the other has occurred, being different from the unconditional probability. Similarly, the influence of one random quantity on another is characterized by the laws for the conditional distributions of the first at fixed values of the second. For each possible value X = x. let the conditional expectation y(x ) = E(y ǀX = x ) of the quantity Y be defined. The function y (x ) is called the regression of the quantity Y on X. and its graph is called the regression line of Y on X. The dependence of Y on X is manifested in the change in the mean value of Y with a change in X. although for each X = x the quantity Y is still a random quantity with a definite scatter. Let my =E(Y ) be the unconditional expectation of Y. If the quantities are independent, then all the conditional expectations of Y are independent of x and coincide with the unconditional expectations:
y(x) = E(YǀX = x) = E(Y) = mY
The converse is not always true. In order to find out how well the regression gives the change in Y with a change in Xt we use the conditional variance of y at a given value of X = x or its mean—the variance of Y relative to the regression line (a measure of the scatter near the regression line):
For a strictly functional relationship, the quantity y at a given X = x assumes only one specific value, that is, the variance near the regression line equals zero.
The regression line may be approximately reconstructed from a sufficiently extensive correlation table: one takes for an approximate value of y (x ) the mean of those observed values of Y that correspond to the valued = x. Figure 1 depicts the approximate regression line corresponding to data in Table 1 for the dependence of the mean diameter of pine trees on height. In the central part this line is obviously a good expression of the actual dependence. If the number of observations corresponding to certain
Table 1. Correlation between the diameters and heights of 624 northern pine trunksSource: encyclopedia2.thefreedictionary.com