WEBVTT
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A concept that's really
important in marketing and
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that also has connections to regression
is something called elasticity.
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Here we are going to
look at price elasticity.
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What it means is, it is the percent change
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in sales for a percent change in price.
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So price elasticity is primarily
change in sales over change
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in price multiplied by price over sales.
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And it is important to have this
value over here, price over sales.
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That is different than
just the coefficient.
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What we saw in regression
was this set here,
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change in sales to change in
price is your coefficient.
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Now if you take the coefficient and
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multiply that by average
price over average sales,
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you would get price elasticity.
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Now, why are we so
hung up on price elasticity?
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Why do we need elasticity?
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It is because elasticity has no units.
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It's unitless, which means every
year you can measure elasticity,
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and track this elasticity over time so
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you can compare improvements or declines
in the effectiveness of your market.
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So that's why it's a really
useful concept to know.
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And we can see how it connects to
regression through this value,
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the coefficient.
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But is there a way to modify,
tweak the regression a little bit
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to just use the coefficient directly and
it will be equal to elasticity?
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Let's see.
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So we're going to take
the example of Belvedere Vodka.
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So far we have looked at made up numbers
and you can say, hey, you're talking about
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made up numbers, I work with real people
with real data give me some real examples.
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So here we go.
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What we have here is data from Belvedere
Vodka over seven years in the US.
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So the data is from 2001 to 2007.
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We have sales of 9 liter cases of
Belvedere Vodka and this is thousands.
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And what we are doing here
is taking from this column
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to this column here, we're taking the log,
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which is the logarithmic
transformation of sales,
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and we are going to look at logarithms and
what they are in a short while.
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But for now,
stay with me to understand that
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logarithm is a transformation
that we make on the data.
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Now, we take a log transformation,
so sales is 410,
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log of sales, is 6.
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This is price of 9 liter cases
of Belvedere Vodka, $215.
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And log of that price is 5.3, and we have
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advertising how much advertising
was done for Belvedere Vodka, and
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this is the log of that advertising value.
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And advertising is also in dollar.
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Thousands.
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So this is real data.
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So far, we have looked at made up data and
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you could be thinking, wait a minute you
are showing me all this with made up data,
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but I am dealing with real people with
real consumers in the real world.
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And does this regression apply in there.
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So here we have it, this is real data
about Belvedere Vodka sales in the US and
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this is real data about the prices
the managers at Belvedere Vodka set and
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how much they advertise in
each of these seven years.
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So we're going to take all of this data
and see the relationship between price and
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sales of Belvedere Vodka, and
apply it into a regression model and
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come up with values that will then give us
a relationship between price and sales.
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So let's see what we got here.
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So here is the output.
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Of the regression of log
of price of Belvedere
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vodka on log of sales of Belvedere vodka.
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So let's see what
the regression output gives us.
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So the R-squared is about 45%,
this is how the data looks like.
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In the x axis, we have price and
in the y axis, we have sales.
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And to be specific,
we have log of price and log of sales.
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That's what we're plugging
into the regression function.
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These green dots are the seven
years of data and
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the black line is your
regression equation.
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Just like we saw in the example.
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Now you know we then need to look at
the coefficients and the p value.
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So the intercept is 12.68.
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So, if price was 0, that would be awesome.
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Free vodka, we all like it.
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If price was 0, then case sales,
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log of case sales of
Belvedere Vodka is 12.6,
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the P-value is less than 0.05,
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which means, what does it mean?
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Think about it.
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Which means, if fee value is low,
high confidence in the regression, right?
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So that's a good thing.
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Now next thing is Ln(Price).
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Coefficient is -1.25,
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P-value is less than 0.1, which is okay.
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It is still lower than
the threshold of 10%.
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It's not great but it's good.
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It will do for now.
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But what do we have here,
this is the coefficient, this the slope,
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this is the change in ln sale for
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change in ln price and
that's the coefficient right here.
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Now here's the kicker,
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when you use ln of price as x and
ln of sales as y
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the coefficient is the same
as price elasticity.
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So now, by doing the log
transformations on the x and y, and
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using that in the regression,
you can actually just do the regression.
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Pick up the coefficient, and that gives
you the elasticity, isn't that cool?
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Now we are going to see,
very shortly, why that is the case.
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Why does doing what is called
a log-log model give you elasticity?