Correlation Analysis

The correlation coefficient provides a numerical measure of the amount of variation in a variable that is attributable to another variable. The correlation analysis function in IC-CAP Statistics generates a complete matrix of correlation coefficients (one for each pair-wise combination of parameters). The correlation values can vary between 1 (perfect positive correlation) and -1 (perfect negative correlation). Uncorrelated variable have a correlation coefficient of 0. The correlation between two variables x and y can be expressed as:

where S_xy is the covariance between the variables and S_x and S_y are the standard deviations of variables x and y respectively.

The correlation matrix is closely related to the covariance matrix of a data set. In fact, the correlation matrix is really nothing more than a covariance matrix with the variances (matrix diagonals) normalized to unity. Under this condition, the denominator in the above equation reduces to one, and the relationship

holds true.

Factor analysis can be applied to either the covariance matrix (unnormalized) or the correlation matrix (normalized covariance matrix). For applications involving semiconductor device model parameters where parameter values may vary over many orders of magnitude, the correlation matrix is preferable, since it weights each parameter variance equally. For this reason, IC-CAP Statistics uses the correlation matrix exclusively as input to factor analysis.

Correlation analysis is always performed before proceeding to factor analysis.