Ordinary Least Squares (OLS) regression is a statistical technique for estimating a relationship between two variables. For example, it can be used to estimate how varying doses of a particular drug relate to reductions in blood pressure, or how hours of tutoring relate to a subsequent increase in SAT scores.

Here is an explanation of OLS with a presentation using calculus and matrix algebra. Here is an explanation for the non quant jock. The title of the poem below is taken from the matrix algebra formula (Wikipedia uses a T superscript where I use a prime (')). The first two lines of the poem restate the title in words if you're baffled about the pronunciation of the title. Only a statistics major or a doctoral student in a good social science program would get into the rigor of the matrix algebra model. When I teach master's students, there's no calculus and no matrix notation. When I teach the one-semester course, the goal is to teach the students to be discriminating consumers of statistical studies that they may see in future public sector employment. In a doctoral course or a year-long master's course, the goal is to teach students how to do their own studies. I've only taught the introductory classes in which I don't have time to give students sufficient experience and depth to develop good studies of their own after they leave. I hope I haven't sent students along armed with a weapon they can't fire properly.

(X’X)

^{-1}X’Y

X prime X inverse

X prime Y

relates phenomenon X

to phenomenon Y.

Umbrella counts on the street

relate to likelihood of rain,

but does rain cause umbrellas,

or do umbrellas cause rain?

Most users of the tool

wouldn’t know the source,

wouldn’t know how their theories

could stray miles off course.

All they know is software

regresses a line,

from that they conclude

that X causes Y:

put X more umbrellas

out on the street,

you’ll get BX more rain,

measured in feet.

&&

## 1 comment:

This is great. Maybe you could publish a collection of "Poetry for Analysts." I'm not kidding. The cynical capitalist in me says that this would be a great Christmas gift.

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