The correlation coefficient is also called the correlation normalized moment, which is the ratio of the correlation moment of the system 2 of random variables (SSV) and its maximum value. In turn, the correlation moment is called the mixed central moment of the second order (MSC X and Y).
Instructions
Step 1
It should be noted that the value W (x, y) will be the joint probability density of the TCO. In turn, the correlation moment will be a characteristic of the mutual scatter of the TCO values relative to a certain point of average values (mathematical expectations my and mx), the level of linear relationship between the indices of free values X and Y.
Step 2
Consider the properties of the considered correlation moment: Rxx = Dx (variance); R (xy) = 0 - for independent exponents X and Y. In this case, the following equation is valid: M {Yts, Xts} = 0, which in this case shows the absence of a linear connection (here we do not mean any connection, but, for example, quadratic). In addition, if there is a linear rigid connection between the values of X and Y, the following equation will be valid: Y = Xa + b - | R (xy) | = bybx = max.
Step 3
Return to the consideration of r (xy) - a correlation coefficient, the meaning of which should be in a linear relationship between random variables. Its value can vary from -1 to one, in addition, it cannot have a dimension. Accordingly, R (yx) / bxby = R (xy).
Step 4
Transfer the obtained values to the graph. This will help you to imagine the meaning of the normalized correlation moment, the empirically obtained X and Y indices, which in this case will be the coordinates of a point on a certain plane. In the presence of a linear rigid connection, these points must lie on a straight line exactly Y = Xa + b.
Step 5
Take the positive correlation values and connect them on the resulting graph. With the equation r (xy) = 0, all designated points should be inside an ellipse with a central region at (mx, my). In this case, the value of the semiaxes of a cent will be determined by the values of the variances of random variables.
Step 6
Take into account that the values of SV obtained by the experimental method cannot reflect the probability density 100%. That is why it is best to use estimates of the required quantities: mx * = (x1 + x2 +… + xn) (1 / n). Then count in the same way as my *.
