# fitting

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## fitting

1. an accessory or part
2. work carried out by a fitter
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Fitting

in statistics, a method by means of which we obtain an analytic and graphic expression of the statistical regularity on which a given empirical series of statistical data is based. By means of fitting, the broken line of the steps of an empirical series is replaced with a smooth, “fitted” curve (in particular cases, with a straight line) and the equation of this curve is computed. During fitting, the following three problems are solved in sequence: the type of equation (shape of the smooth curve) is selected, the parameters (coefficients) of this equation are computed, and the levels (ordinates) of the “theoretical” statistical series obtained are computed (on the basis of the equation) or measured (by the graph of the curve). The type of equation and, correspondingly, the shape of the smooth curve are selected on the basis of general in-formation about (or frequently from practical experience with) the essence of the phenomenon, the regularities of its structure and development, the relationships among its attributes, and so forth (so-called analytic fitting). Where such advance information is not available, the type of equation (shape of the curve) can often be suggested by the graphic shape of the broken line that expresses the given empirical series.

In socioeconomic statistics, fitting is used in three typical cases: (1) fitting a series of distributions, (2) fitting broken lines of regression, and (3) fitting series in a dynamic process.

The purpose of fitting series of distributions is to give quantitative and graphic expressions for the nature of the regularity of the distribution of units of the aggregate on the basis of an assigned attribute (for example, their normal distribution and distribution according to Poisson’s law). In this we preserve the equality of certain primary numerical characteristics of the given empirical series and the theoretical series obtained: the average magnitude of the attribute, the mean quadratic deviation, and the total number of units in the aggregate. We use a particular goodness-of-fit test to establish the degree to which the levels (ordinates) of the theoretical series obtained correspond in aggregate to the empirical steps. In some special cases, for example when fitting population distribution by age given in the census, specially developed procedures and formulas are used to eliminate the well-known “accumulation of ages” ending in 0 and 5. Fitting distributions always assumes the availability of a sufficiently numerous empirical series of data.

Fitting broken lines of regression is done when studying the relationships of attributes in order to obtain a smooth line of regression and a regression (correlation) equation that ex-presses the dependence of the average values of one attribute on values of others; for example, yx = a + bx; yx,z = a + bx + cz.

We resort to fitting time series in dynamic processes to obtain an equation (and a smooth line) expressing the developmental trend of a process in time t; for example, y = a + bt, y = a + bt + ct2. In the last two cases of fitting, the coefficients a, b, c, … of the unknown equation are usually computed by the method of least squares. The fitting of statistical time series should not be confused with smoothing statistical series.

### REFERENCES

Huntington, E. V. “Vyravnivanie krivykh po sposobu naimen’shikh kvadratov i sposobu momentov.” In Matematicheskie melody v statistike. Collection of articles edited by H. L. Rietz. Translated and reworked by S. P. Bobrov. Moscow, 1927. Pages 147-61.
Ezhov, A. I. Vyravnivanie i vychislenie riadov raspredelenii. Moscow, 1961.
Khotimskii, V. I. Vyravnivanie statisticheskikh riadov po metodu naimen’shikh kvadratov (sposob Chebysheva). Moscow-Leningrad, 1925. Second ed., Moscow, 1959.
Chetverikov, N. S. “O tekhnike vychisleniia parabolicheskikh krivykh.” In Voprosy kon“iunktury, vol. 2. Moscow, 1926. Reprinted in Chetverikov’s book Statisticheskie i stokhasticheskie issledovaniia. Moscow, 1963. Pages 190-210.
Iastremskii, B. S. Nekotorye voprosy matematicheskoi statistiki. Moscow, 1961. Chapter 2.
Obukhov, V. M. “K voprosu o nakhozhdenii uravneniia regressii, udoletvoriaiushchego dannomu empiricheskomu riadu.” Trudy TsSU, vol. 16, issue II. Moscow, 1923.

F. D. LIVSHITS

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.

## fitting

[′fid·iŋ]
(building construction)
(engineering)
A small auxiliary part of standard dimensions used in the assembly of an engine, piping system, machine, or other apparatus.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## fitting

fittings, 1
1. A pipe part, usually standardized, such as a bend, coupling, cross, elbow, reducer, tee, union, etc.; used for joining two or more sections of pipe together. The term usually is used in the plural.
2. An accessory such as a bushing, coupling, locknut, or other part of an electric wiring system which is intended to perform a mechanical rather than an electrical function.
3. Same as window hardware.
4. British for luminaire.
5. A decorative or functional item or component in a building which is fixed but not built in; also called a fitment.
McGraw-Hill Dictionary of Architecture and Construction. Copyright © 2003 by McGraw-Hill Companies, Inc.
References in periodicals archive ?
Therefore, scholars need not to be guided by the principle of generalizability rather they should be guided by the principles of fittingness and comparability when they deal with aspects of cultural that seem to apply to different African cultures.
If the experience of logical 'correctness' is the experience of a certain kind of fittingness, so that the 'ugliness' of a painting and the 'ugliness' of an inference are in some sense continuous, then the perception of the logical force of reason is a special case or range of an aesthetic responsiveness to what may be described as [TEXT NOT REPRODUCIBLE IN ASCII].
He covers Christological methods, the election of Jesus Christ, the pre-existence of Christ, the fittingness of the virgin birth, Christ and the embryo, whether Christ was sinless or impeccable, materialist Christology, and multiple incarnations.
Father Moss added: "You really sense a lovely kind of continuity and fittingness."
Respect as fittingness is the idea that each person is entitled to be treated in accordance with his status concerning some specified attribute.
"A certain fittingness of world to mind [convenientia entis ad intellectum]" thus yields what Fergus Kerr calls a "radically non-interiorist account of the self," one that no longer involves some hermetic Cartesian cogito wrestling with medium-sized dry goods.
Following Roberts and Taylor (2002) the qualitative studies in this review were further evaluated using categories of credibility, fittingness, auditability and confirmability to determine rigour or 'validity and reliability'.
(21) Furthermore, it explains why cultural creations have a sense of fittingness and context.
Qualitative research: The evaluation of its credibility, fittingness, and anditability.
Even if we recognize that there is a certain fittingness in the inner pain a criminal feels in his separation from the good he rejects and violates, one can still claim that punishment is a matter left to the final judgment of God.
Scientific rigor was achieved through credibility, audibility, and fittingness (LoBiondo-Wood & Haber, 2005).

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