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A mathematical technique used to explain and/or predict. The general form is Y = a + bX + u, where Y is the variable that we are trying to predict; X is the variable that we are using to predict Y, a is the intercept; b is the slope, and u is the regression residual. The a and b are chosen in a way to minimize the squared sum of the residuals. The ability to fit or explain is measured by the R-square.

Regression Analysis

In statistics, the analysis of variables that are dependent on other variables. Regression analysis often uses regression equations, which show the value of a dependent variable as a function of an independent variable. For example, a regression could take the form:

y = a + bx

where y is the dependent variable and x is the independent variable. In this case, the slope is equal to b and a is the intercept. When plotted on a graph, y is determined by the value of x. Regression equations are charted as a line and are important in calculating economic data and stock prices.


(1) A statistical technique for creating a mathematical equation to explain the relationship between known variables so that the model can be used to predict other variables when one has insufficient data. Multiple regression analysis is the basis of computerized automatic valuation models (AVM) employed instead of appraisals by many mortgage lenders. (2) An appraisal principle that if properties of relatively unequal value are located near each other, the one with the lower value will depress the value of the other. (3) A withdrawal of the sea from the land due to an uplift of the land or a drop in sea level.

References in periodicals archive ?
The regularization parameter ([gamma]) controls the penalty imposed to data points that deviate from the regression function.
1, C = 10 and the linear kernel, construct support vector regression, we can get regression function [[phi].
These results on the regional dummies and the time trend taken together suggest that a two-way fixed-effects model of the regression function is reasonable.
The correlation method gathers in its current state the whole complex of identification for causal links between phenomena and investigation of statistical connections, leading to synthetic numeric representations: regression functions, regression coefficients, correlation coefficients, determination coefficients, estimation errors etc.
Uniform Convergence Rates of the Wavelet Estimator of Regression Function Under Mixing Error, Acta Mathematica Scientia, 22A(2002), 528-535.
Table 3 provides maximum-likelihood estimates from the multiplicative heteroscedasticity model (20) of various specifications of the basic regression function posited in Equation 1 and the corresponding variance functions.
Figure 3 plots the markets' average sales reallocation and the estimated regression function against the logarithm of the HHI.
ii) The absolute residuals are obtained from the fitted model in (i), and the regression function for these absolute residuals identified.
The outlying or extreme cases may involve large residuals and have dramatic effects on the fitted least square regression function.
ij]) is the estimator of regression function [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is Nadaraya--Watson--type weight, K is a known kernel, h is an appropriate bandwidth, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be an estimator of the common regression function m(x) = [m.
On the Asymptotic Normality for [phi]-mixing Dependent Errors of Wavelet Regression Function Estimator, Acta Mathematicae Applicatae Sinica, 31(2008), No.
The statistical analysis allowed the determination of the mutual correlation between X and Y, and the regression function type that approximated a certain set of points.