# regression analysis

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Related to Population regression function: regression analysis

## re·gres·sion a·nal·y·sis

the statistical method of finding the "best" mathematical model to describe one variable as a function of another.

## re·gres·sion a·nal·y·sis

(rĕ-greshŭn ă-nali-sis)The statistical method of finding the "best" mathematic model to describe one variable as a function of another.

## regression analysis

(in statistics) a test in which the size of one variable (the dependent variable) is dependent on another (the independent variable). Often the relationship is a linear one, enabling a line of best fit to be drawn on a SCATTER DIAGRAM.## re·gres·sion a·nal·y·sis

(rĕ-greshŭn ă-nali-sis)The statistical method of finding the "best" mathematic model to describe one variable as a function of another.

## regression analysis,

*n*a method of correlation for computing the most probable value of one variable,

*y,*from the known value of another variable,

*x;*a method for computing the amount of change in one variable for a unit change in another. It is spoken of as the regression of

*x*on

*y*and notated

*r*

_{xy}.

## analysis

separation into component parts.

**cohort analysis**

the separation of each of two cohorts into component parts and comparing the results.

**current analysis**

analysis performed on contemporary data.

**discriminant analysis**

a form of multivariate analysis in which the objective is to establish a discriminate function. The function (typically a mathematical formula) discriminates between individuals in the population and allocates each of them to a group within the population. The function is established on the basis of a series of measurements or observations made on the individuals.

**economic analysis**

evaluation of the costs and benefits of a commercial enterprise that takes into account additional returns, returns no longer obtained, additional costs and costs no longer incurred, discounting of gains back to the time when the project began, and opportunity costs relating to potential profitability from alternative use of the investment.

**factor analysis**

a multivariate technique which analyzes the underlying structure of a set of data. It is useful in explaining observed relationships amongst a large number of variables in terms of simpler relations.

**guaranteed analysis**

declares the range within which nutrients occur in a manufactured animal food.

**multivariate analysis**

techniques for the study of simultaneous variation in a number of variables. Includes linear discriminant functions, cluster analysis and factor and principal component analysis.

**path analysis**

a statistical technique for testing a limited number of causal hypotheses, the causal relationships between variables, by manipulation of one or more of the variables and predicting the outcome.

**qualitative analysis**

determination of the nature of the constituents of a compound or mixture.

**quantitative analysis**

determination of the proportionate quantities of the constituents of a compound or mixture.

**regression analysis**

a general statistical technique that analyzes the relationship between a dependent (criterion) variable and a set of independent (predictor) variables.

**systems analysis**

analysis of the interaction of a system, e.g. a biological system, often for the purpose of analyzing the differences between systems. See also system.

**analysis of variance**

a statistical method for comparing variables by partitioning the variance of the observations between the effects of the different variables and comparing it with the underlying random variation.

**vector analysis**

analysis of a moving force to determine both its magnitude and its direction, e.g. analysis of the scalar electrocardiogram to determine the magnitude and direction of the electromotive force for one complete cycle of the heart.

## regression

1. return to a former or earlier state.

2. subsidence of clinical signs or of a disease process.

3. in biology, the tendency in successive generations toward the mean.

4. the relationship between pairs of random variables; the mean of one variable and its location is influenced by another variable.

**regression analysis**

see regression analysis.

**regression coefficient**

is the factor which determines the slope of a regression line; the greater the coefficient the steeper the line.

**curvilinear regression**

when the relationship between two variables is not linear.

**linear regression**

the relationship between two variables is a straight line.

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