The correlation model (CM) is a calculation program that provides a mathematical equation in which the effective indicator is quantitatively determined depending on one or more indicators.
yx = ao + a1x1
where: y is an effective indicator depending on the factor x;
x is a factor sign;
A1 is the KM parameter, showing how much the effective indicator y will change when factor x changes by one, if all the other factors affecting y remain unchanged;
ao-parameter KM, which shows the influence of all other factors on the effective indicator y, except for the factor sign x
When choosing the effective and factorial indicators of the model, it is necessary to take into account the fact that the effective indicator in the chain of causal relationships is at a higher level than factor indicators.
Characteristics of the correlation model
After calculating the parameters of the correlation model, the correlation coefficient is calculated.
p is the coefficient of pair correlation, -1 ≤ p ≤ 1, shows the strength and direction of influence of the factor indicator on the effective one. The closer to 1, the stronger the connection, the closer to 0, the weaker the connection. If the correlation coefficient has a positive value, then the relationship is direct, if negative - the inverse.
Correlation coefficient formula: rhu = (xy-x * 1 / y) / eh * eu
eh = xx2- (x) 2; eu = y2- (y) 2
If KM is linear multifactor, having the form:
yx = ao + a1x1 + a2x2 + ... + aphp
then a multiple correlation coefficient is calculated for it.
0 ≤ P ≤ 1 and shows the strength of the influence of all combined factor indicators on the effective.
P = 1- ((woo-woo) 2 / (woo-woo) 2)
Where: uh - effective indicator - estimated value;
yi - actual value;
averaged actual, average.
The calculated value of yx is obtained by substituting in the correlation model instead of x1, x2 etc. their actual values.
For one-factor and multifactor non-linear models, the correlation ratio is calculated:
-1 ≤ m ≤ 1;
0 ≤ m ≤ 1
It is believed that the relationship between the effective and factorial indicators included in the model is weak if the value of the coefficient of communication tightness (m) is in the range 0-0.3; if 0.3-0.7 - the tightness of communication is average; above 0.7-1 - the connection is strong.
Since the correlation coefficient is (paired) p, the correlation coefficient is (multiple) P, the correlation ratio m are probabilistic quantities, then the coefficients of their materiality are calculated for them (determined from the tables). If these coefficients will be greater than their tabular value, then the coefficients of tightness of communication are significant reasons. If the coefficients of materiality of the tightness of communication are less than the tabular values, or if the coefficient of communication is less than 0.7, then not all factor indicators that significantly affect the result are included in the model.
The coefficient of determination clearly demonstrates how many percent the factor indicators included in the model determine the formation of the result.
D = P2 * 100%
D = P2 * 100%
L = m2 * 100%
If the coefficient of determination is greater than 50, then the model adequately describes the process under study, if it is less than 50, then we must return to the first stage of construction and review the selection of factor indicators for inclusion in the model.
The Fisher coefficient or Fisher criterion characterizes the effectiveness of the model as a whole. If the calculated value of the coefficient exceeds the tabulated one, then the constructed model is suitable for analysis, as well as planning indicators, long-term calculations. Roughly tabular value = 1.5. If the calculated value is less than the tabulated value, it is necessary to build the model first, including factors that significantly affect the result. In addition to the effectiveness of the model as a whole, each regression coefficient affects the materiality. If the calculated value of this coefficient exceeded the tabulated value, then the regression coefficient will be significant, if lower, then the factor indicator for which this coefficient is calculated is removed from the sample, the calculations are started again, but without this factor.