implies we are using a set of mathematical rules called matrix algebra, and that’s not entirely

incorrect. Mathematical descriptions of multiple regression (covered in Chapter 17 of this book)

make extensive use of matrix algebra. Also, computer software may refer to tabular objects with

the term matrix.

Arrays in formulas

If you see an array name in a formula without any subscripts, it usually means that you have to evaluate

the formula for each element of the array, and the result is an array with the same number of elements.

So, if Gluc refers to the array with the five elements 86, 110, 95, 125, and 64, then the expression 2 ×

Gluc results in an array with each element in the same order multiplied by two: 172, 220, 190, 250,

and 128.

When an array name appears in a formula with subscripts, the meaning depends upon the context. It can

indicate that the formula is to be evaluated only for some elements of the array, or it can mean that the

elements of the array are to be combined in some way before being used (as described in the next

section).

Sums and products of the elements of an array

This Greek letter ∑ is known in English as capital sigma. Though harmless, ∑ strikes terror into the

hearts of many learners as they encounter it statistics books and articles (not to mention its less

common but even scarier cousin Π, also known as capital pi). Uppercase sigma and pi — namely ∑

and Π — correspond to the Roman letters S and P, which stand for Sum and Product, respectively.

These symbols are almost always used in front of variables and expressions that represent arrays.

When you see ∑ in a formula, just think of it as saying “sum of.” Assuming an array named Gluc that is

comprised of the five elements 86, 110, 95, 125, and 64, you can read the expression

as “the

sum of the Gluc array” or “sum of Gluc.” To evaluate it, add all five elements together to get

, which equals 480.

Sometimes the ∑ notation is written in a more complex form, where the index variable i is displayed

under (or to the right of) the ∑ as a subscript of the array name, like this:

. Though its meaning

is the same as

, you would read it as, “the sum of the Gluc array over all values of the index i”

(which produces the same result as

, which is 480). The subscripted ∑ form is helpful in

expressing multi-dimensional arrays, when you may want to sum over only one of the dimensions. For

example, if Ai,j is a two-dimensional array:

then

means that you should sum over the rows (the i subscript) to get the one-dimensional

array: 35, 23, and 34. Likewise,

means to sum across the columns (j’) to get the one-

dimensional array: 58, 34.

Finally, you may see the full-blown official mathematical ∑ in all its glory, like this:

which reads “sum of the Gluc array over values of the index i going from a to b, inclusive.” So if a

was equal to 1, and b was equal to 5, the expression would become: