Correlation is used to estimate the tightness and direction of the linear stochastic dependency between analyzed variables. Linear stochastic dependency of random variables means that when a random variable increases, the other one tends to increase (or decrease) in linear fashion. This linear dependency tendency can be more or less pronounced, that is, more or less approach the functional dependency.
Given below is the equation used to calculate correlation coefficient:
Where:
-1 ≤ ρx,y ≤ 1
is a covariance, that is, the mean of deviation products for each pair of data points.
x and y are sample averages.
Paired coefficients are calculated following the formula:
Correlation between two random variables calculated with the fixed levels of all other variables is named partial correlation. For the three variables Y1, Y2, X3 partial correlation between the variables Y1, Y2 is estimated following the formula:
Where ρ is the paired correlation coefficient.
In this case, partial correlation coefficient measures linear correlation between the variables Y1, Y2, excluding separate contributions of linear relationships of Y1, Y2 with the third variable X3.
Generally, let the set of variables be divided into two groups Y and X with nY variables in the set Y, and nX variables in the setX.
Let us represent covariance matrix as:
The covariance Y with fixed values of X:
The matrix of partial correlation coefficients:
See also:
Library of Methods and Models | IStatistics.Correl | IStatistics.Covar | ISmPairCorrelation | ISmPartialCorrelation