There is not one universal criterion for the selection of the number of principal components. For that reason it is recommended to make the selection with the help of several methods.

• The percentage of explained variance

The number of principal components to be assumed by the researcher depends on the extent to which they represent original variables, i.e. on the variance of original variables they explain. All principal components explain 100\% of the variance of original variables. If the sum of the variances for a few initial components constitutes a large part of the total variance of original variables, then principal components can satisfactorily replace original variables. It is assumed that the variance should be reflected in principal components to the extent of over 80 percent.

• Kaiser criterion

According to the Kaiser criterion the principal components we want to leave for interpretation should have at least the same variance as any standardized original variable. As the variance of every standardized original variable equals 1, according to Kaiser criterion the important principal components are those the eigenvalue of which exceeds or is near value 1.

• Scree plot

The graph presents the pace of the decrease of eigenvalues, i.e. the percentage of explained variance.

The moment on the chart in which the process stabilizes and the decreasing line changes into a horizontal one is the so-called end of the scree (the end of sprinkling of the information about the original values carried by principal components). The components on the right from the point which ends the scree represent a very small variance and are, for the most part, random noise.