Analysis of multiple correlation

For the research of two or more factors influence on the change of the resulting parameter, the multiple correlation takes place. At that matter, both the rectilinear and curvilinear equations of regression are used.

The supposition about the existence of the multiple correlation linear equation can be represented as this:

The separate coefficients of the regression equation characterize the influence of the respective factor on the resulting parameter, at the condition of other factors elimination.

The term of the equation doesn't have any economic content and can't be interpreted.

At studying of the multiple correlative connection of the resulting attribute, say, with two factorial ones, the analytical equation of regression looks like this:

The parameters of the multiple regression equation ( ) are calculated by the system of normal equations:

The parameters of the connection tightness at the multiple correlation are thepaired, the partial, the multiple coefficients of correlation, the multiple coefficient of determination and the partial coefficients of determination.

Paired coefficients of correlation characterize the tightness of connection between two attributes without the consideration of their interaction with other attributes:

Partial coefficients of correlation characterize the tightness of the connection between the resulting attribute and one factorial attribute at the condition that other factorial attributes are at the same constant level:

Multiple coefficient of correlation characterizes the tightness of connection between all the researched factors of a model:

Multiple coefficient of determination is calculated by the formula:

In its turn, the multiple coefficient of determination is decomposed to the partial coefficients of determination which characterize the degree (percentage) of the resulting attribute dependence from the variation of each factorial attribute:

In addition to that, the importance checkout of the multiple coefficient of correlation (by the F-criterion) and the regression coefficients (by the ) might be done.

I uninstalling one value from a statistical aggregate. It is at number 17 and is the highest in the aggregate. I do it because otherwise the limit is not met the .

So I have a set of statistics:

TABLE 21

A set of statistics

№
	1625,2	2298,9	55,7
	1530,3	1463,3	52,5
	885,7	1589,5
	482,3	1250,6	59,5
	1300,8	1617,5	50,7
	1241,5	1209,6	49,3
	822,3	988,3	54,9
		1400,3	43,6
	884,7		68,5
	762,9	1665,6	56,5
	1620,1	1369,4	45,9
		1234,6
	689,1	1635,6	48,2
		1974,7
	666,6	822,3	53,5
	1126,8	1071,5	45,8
	495,6	1022,4	49,7
	1114,4	1288,1	47,5
	1298,8	1522,6	56,2
	778,7	1350,5	53,6
		1176,2	49,8
	878,6	820,5	52,8
	1485,7	1433,5	44,9
		2093,5	49,5
	524,6	1124,1	46,1

TABLE 22

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