Typically, these are more convenient to measure than the values we wish to model. The Y variables are the quantities we wish to predict in future. These will be the values estimated from the X values using the model. This is a measure of the spread of a variable about its average value. This is a measure of the similarity of two variables.
Variables having high covariance are strongly related to each other.
To know the strength of this relationship, we also need to know the variance of the individual variables. If, for each variable, we measure n samples, and write the measured values as columns of a table, we refer to this table as a matrix. A mathematics of matrices can be defined, such that we can multiply tables by each other, add tables together, etc. Multivariate calibration depends strongly on this representation. To transpose a matrix, simply write its rows as columns.