Okay, so there is my linear model.

Don't let that scare anybody!

If that scares you, just go back and look at the regression video, and

I think in a few minutes you'd be comfortable with this again.

And what's in this regression model?

Well, it's generally what's called a demand model, so

you have how much beef is sold over here?

That's what's called my dependent variable.

And then I have a series of independent variables,

these are the things that we believe might impact beef sales.

That's why they are in the model.

The first one X1 here is defined as my own price and

that's pretty straight forward, right?

What I'm charging for the beef that affects how much I'm selling of the beef.

The second is the price of a related good and in this case, chicken.

We might believe that the price of chicken might impact beef sales one way or

the other, that's why it's in the model.

And then we have a measure of disposable income.

So, what's that going to answer is when people have more money,

do they buy more or less of this particular cut of beef?

And finally what's called a trend variable.

And that was covered in the regression model,

it's simply a very simple time trend variable.

Just to account for the fact that it might be the case that beef sales are growing or

shrinking over time for reasons unrelated to price.

So we need to put that in there.

So now we are going to perform a linear regression.

We are going to estimate the model.

Okay and we did some

initial analysis on the beef prices and this is a chuck roast in particular.

And we did some initial analysis with the chicken to make sure that

the data was suitable to put it into the model.

Here is the estimated model.

The model is reproduced down below, but

what you see are the estimated coefficients.

Those beta coefficients, those coefficients measure

how sensitive the dependent variable, in this case the quantity sold of this chuck,

this beef, Is to the particular variables in the model.

That's the way you interpret it.

So there it is for chuck, and it's negative and

you would expect it to be negative.

That just means the demand curve is downward sloping.

The higher price I charge, or the less people buy.

I've got a chicken price, also a negative coefficient and income and trend.

And if I look over here on the right hand side,

if you recall from the regression video, that we can look at the t

statistics to determine what is significant and what isn't.

And chuck price is significant.

Income is significant.

And trend is significant.

Chicken price is kind of marginally significant, not overly significant.

Okay.

Now, what can we do with this?

We can calculate the price elasticities, cross price elasticities, and

income elasticities.

In this video I'm just going to look at the price elasticities and then

I can also take that information and use the estimated model as a demand function.

Okay, more about that later.

And then I could also compute the optimal price of this cut of beef

under different scenarios.

But right now, I mean we're going to do all this, but

right now I'm going to focus on price elasticity.

So remember the definition of price elasticity.

Percentage change in quantity divided by percentage change in price.

It can be written as that.

Delta just means change in Q divided by Q, that's the percentage change.

Delta P divided by P, and rearranging that gives us this definition right here.

What's nice about that is I know this, the change in Q divided by the change in P.

And I know that, because that is coming from the regression model,

that's the estimated coefficient, this -50.16.

I can then use that estimated coefficient and multiply that by P over Q right?

From the definition, and I get the P and the Q out of the means of the data.

So the mean price and the mean quantity of chuck sales.

If I compute the mean across all the data the average for chuck for any given month,

it's 107.54 and that's an index number that relates to the number

of pounds that are sold and the average price is $2.47 per pound.

So I can then put that back into the model -50.16, insert those means.

That gives me -1.15 and how is that interpreted?

At its most basic level the way that's interpreted is a 10% change in

price will be associated with approximately 11.5% change in quantity.

Or you could say a 1% change in price will lead to a 1.15% change in quantity.