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Well, the last thing that I, I want to cover in this module is the fact that
we've looked at a very simple notion of errors, this residual sum of squares.
And it's actually really, really commonly used in practice.
But we're gonna talk a lot more about
different types of errors later in the course.
But I wanted to go through some of the intuition of what happens if we
use a different measure of air.
Okay so this residual sum of squares that we've been looking at
Is something that's called a symmetric cost function.
And that's because what we're assuming when we look at this aerometric
is the fact that if we over estimate the value of our house,
that has the same cost as if we under estimate the value of the house.
And the question is so we actually believe that is the case?
And what happens if there might not be symmetric cost to these error?
But what if the cost of listing my house sales price
as too high is bigger than the cost if I listed it as too low?
So for example, if I list the value as too high,
then maybe no one will even come see the house.
Or they come see it and they say oh it's definitely not worth it.
I'm not putting in an offer.
So the result might be I get no offers.
So as a seller, that's a big cost to me.
I've gone through this whole thing of trying to sell my house.
I want or need to sell my house.
And I get no offers.
On the other hand,
if I list the sales price as too low, of course I won't get offers as high
as I could have if I had more accurately estimated the value of the house.
But I still get offers, and
maybe that cost to me Is less bad than getting no offers at all.
For example if I have to move to another state I have no choice but
to sell my house.
Okay, so
in this case it might be more appropriate to use an asymmetric cost function
where the errors are not weighed equally between these two types of mistakes.
And instead of this dash orange line here,
which represents our fit when we're minimizing residual sum of squares.
I will get some different solution.
Again, sorry, I love to write over my animations.
Here this is the fit minimizing residual sum of squares, and
this other orange line here is this other solution using an asymmetric loss.
Asymmetric Loss and specifically in asymmetric loss.
Let me just say asymmetric cost.
Where I prefer to underestimate the value than over.
And that's what you see here is, in general,
we're predicting the values as lower.
As compared to the line that we got or our predictions using residual sum of squares.
Okay so that's just a little bit of intuition about what would happen using
different cost functions and
again we're gonna talk a lot more about this later on in this course.
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