And so, let's go back to thinking about the weight of a diamond,

and the price that it's going to go for.

And so, often times we think of representing,

the model that we have through some graphical approach.

And so, in this course I'm going to be using a lot of graphics because they

are perhaps the most elegant way to produce, and

represent, and share your models with other people.

And so what you're looking at here is a graph where on the horizontal axis,

we often call that the x-axis,

you have the weight of the diamond that is measured in carats, and

on the vertical axis you have the expected price of the diamond.

And what I'm looking at here is a potential model.

It's a very straightforward model, it's what we term a linear

model because it's a straight line, and I have the equation

associated with the model at the bottom of the slide here.

And what I'll do later on is, discuss in much more detail such a linear equation,

but right now I just want to show you that given such a model, you would be able to

use it to help forecast the expected price of a diamond.

And so if, for example, I'm looking at a diamond ring that weighs 0.3 of a carat,

all that I need to do is go into this graph, identify the 0.3 on the horizontal

axis, go up to the graph itself, the line, read off the value on the vertical axis

that we often call the y-axis, and there I have an expected price for a diamond.

And so in this particular case, we've got a linear model.

It's not clear that that's going to work for all diamonds,

but if you have a look at the range of the x-axis here, it's somewhat limited.

These are diamonds between 0.15 and 0.35 of a carat,

it's the realm that I'm going to apply this model.

I'm not saying that it necessarily applies to the diamond that weighs one carat or

two carats way outside the range, but it might be reasonable

that within this limited range one would see a linear relationship.

So that's an example of what we call a linear model.