Let's talk now a little bit about interpretation of

the regression coefficients.

So when you have a quantitative model, be it a deterministic or a probabilistic

model, it is always a good idea to interpret coefficients if you're able to.

Because by interpreting those coefficients you're going to be out to articulate to

other people what your model is doing in a much more understandable way.

If you just present other people with mathematical equations, and

the sad reality is that a lot of people are going to turn off.

If you can interpret what those equations mean,

then you have chance of a conversation.

So, here's a third regression.

In this particular regression, what we've taken is a production process.

And each point in the scatter plot is telling you about a particular run

of that production process.

On the horizontal axis, or the x-axis, we have the size of the run.

The number of units produced.

On the vertical axis, we have the time that it took to do that run.

So we've got time to produce against run size.

We look at the data points.

And that's quite a lot of noise in those data points but

a reasonable starting model is a linear model.

So we fit a regression to those data points.

Now, that we've got a regression equation and I've written down the regression

equation, it's formally E(Y|X) = 182 + 0.22 X.

So we got an intercept of 182 and a slope of 0.22.

And that left-hand side of the equation, the E(Y|X),

is to be understood as the expected or the average run-time for a given size of job.

And such an equation would be useful if for

example you had a customer coming in, a potential customer who says,

I've got a job that's of 1,000 units, when are you going to have it done for me?

And an equation like this could be part of that decision making process,

the decision support tool idea of quantitative models.

So what I want to do though right now is interpret the coefficients in this

equation.

Now, interpreting the coefficients is really facilitated

by looking at the units of measurement.

So we've got two variables here, a Y and an X, and both has a unit of measurement.

The X variable is the number of items produced.

And the Y variable is the time for the run in minutes.

So, Y is measured in minutes and X is in items.

So, if we equate units on both sides, you can see that the units of a 182, they

have to match the units of the left-hand side, so that's measured in minutes.

So the intercept is going to be measured in the units of Y, which is minutes.

Whereas the slope, the 0.22, because it's been modified by X,

which is measured in items, must be in minutes per item.

So generally, the slope is going to have units to Y/X.

That shouldn't be surprising.

Slope is often articulated as rise over run.

Rise has units of Y.

Run has units of X.

So the slope is measured in units of Y/X.

In this particular instance, we've got 182 being measured in minutes.

It's the time it takes to do a job of no size.

Now, you might think that's crazy, but probably better to say,

it's that part of the time for the job that doesn't depend on the run size.

That, we would view as the set up, or start up time.

So we got a 182 minute set up time.

That says it takes about three hours to set up one of these machine for

the process.

And then once the machine is set up it's 0.22 of a minute.

0.22 is about a quarter.

That's about 15 seconds roughly per incremental or additional item.

And I might term that the work rate.

I like using the word rate when I talk about a slope because a slope is a rate

of change.

So, this is something you want to try to do with your regression coefficients.

Interpret them in the context to the problem

if they lend themselves to interpretation.

So, in this example we got an intercept as a setup time and slope as a work rate.

The underlying idea of equating the units of analysis on both sides of the equation

really is a helpful approach to interpreting

coefficients in a regression equation.

So, strive to interpret those regression coefficients.