# The correlation coefficient - characteristic correlation model

Correlation model (CM) - a program computing, providing the production of a mathematical equation, in which productive indicator quantified depending on one or more indicators.

uh = ao + a1h1

where: y - effective rate, depending on the x factor;

x - factor variable;

A1 - KM option, showing how much productive indicator will change from a change of factor X per unit, provided that all other factors affecting y remain unchanged;

AO parameter KM which shows the influence of all other factors on a productive indicator at other than factor variable x

When choosing effective indicators and factor models must take into account the fact that the productive indicator in the chain of causality is at a higher level,factor than performance.

specifications correlation model

After calculating the parameters of the model calculated the correlation coefficient of correlation.

r - correlation coefficient, -1 ≤ p ≤ 1, shows the strength and direction of the influence factor on the index score.The closer to 1, the stronger the relationship, the closer to 0, the weaker link.If the correlation coefficient is positive, then a direct connection if negative - feedback.

correlation coefficient formula pxy = (x * x-1 / y) / * eu eh eh

hh2- = (x) 2;eu = y2 (y) 2

If KM linear multifactorial, having the form:

uh = ao + a1h1 a2x2 + ... + anx

then it is calculated multiple correlation coefficient.

0 ≤ p ≤ 1, and shows the strength of the combined influence of all parameters on a productive factor.

P = 1- ((uh-yi) 2 / (yi -usr) 2)

Where: uh - productive indicator - calculated value;

yi - the actual value;

usr- actual value of the average.

Estimated value yi obtained by substituting the correlation model instead of x1, x2 etc.their actual values.

for univariate and multivariate nonlinear models calculated correlation ratio:

-1 ≤ m ≤ 1;

0 ≤ m ≤ 1

believed that the relationship between productive and included in the model of factorial indicators is weak, if the value of the coefficient closeness of the connection (m) in the range 0-0.3;if 0.3-0.7 - the tightness of connection - the average;above 0.7-1 - a strong bond.

Since the correlation coefficient (steam) p, the correlation coefficient (multiple) P correlation ratio m - values ​​of probability, then they expect the coefficients of their importance (determined by the table).If these factors are greater than the value of the table, the closeness of the connection coefficients are significant factors.If the factors of importance closeness of the connection is less than the tabulated values ​​or if he coupling coefficient is less than 0.7, the model does not include all performance factor significantly influencing the outcome.

determination coefficient demonstrates the percentage factor included in the model parameters determine the formation of the result.

D = P2 * 100%

D = P2 * 100%

D = m2 * 100%

If the coefficient of determination is greater than 50, then the model adequately describes the process under study, if less than 50, then we must go back to the first stage of constructionand to revise the selection factor indices for inclusion in the model.

ratio Fisher or Fisher test characterizes the efficiency of the model as a whole.If the calculated ratio is greater than the table, the built model is suitable for the analysis and planning of indicators of calculations for the future.Roughly table value = 1.5.If the calculated value is less than the table, you must first build a model, including significant factors influencing the result.In addition to the efficiency of the overall model to significantly affect each regression coefficient.If the calculated value of this ratio exceeded the largest table, the regression coefficient is significant, if less, the factor index, which is designed for this ratio, are removed from the sample, the calculations begin at first, but without this factor.