Uncorrected Sums of Squares and Cross Products Matrix (USSCP)

The Data Matrix The most important matrix for any statistical procedure is the data matrix. The observations form the rows of the data matrix and the variables form the columns. The most important requirement for the data matrix is that the rows of the matrix should be statistically independent. That is, if we pick any single row of the data matrix, then we should not be able to predict any other row in the matrix. Practically speaking, statistical independence is guaranteed when each row of the matrix is an independent observation. To illustrate the data matrix and the other important matrices in this section, let us consider a simple example. Sister Sal of the Benevolent Beatific Bounty of Saints Boniface and Bridget was the sixth grade teacher at The Most Sacred Kidney of Saint Zepherinus School. During her tenure there Sister Sal not only kept track of the students' grades but also wrote down her own rating of the chances that a student will eventually grow up to become an ax murderer. Below is a table of five of Sister Sal's students, their age in sixth grade, Sister Sal's ax murder rating, and their scores as adults on the Psychopathic-deviate scale on the Minnesota Multiphasic Personality Inventory (MMPI Pd).