Unit 5 33 Linear RegressionYouTube↗  IA↗(long shot)
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now obviously you can answer this question without understanding anything
Now obviously you can answer this question without understanding anything about regression.
about regression but what you find is this is different from classification as
But what you find is this is different from classification as before.
before this is not a binary constant many more of like expensive and cheap
This is not a binary concept anymore of like expensive and cheap.
it's really a relationship between two
It really is a relationship between two variables.
variables one you care about the house price and one that you can observe which
One you care about--the house price, and one that you can observe,
is the house in the size and square feet
which is the house size in square feet.
and your goal is to really fit a curve that best explains the data once again
And your goal is to fit a curve that best explains the data.
we have a case where we can play offense
Once again, we have a case where we can play Occam's razor.
raiser there's keenest with its nonlinear that
There clearly is a data fit that is not linear that might be better,
might be better like this one over here
like this one over here.
and when I go to highly nonlinear curves
And when you go to hide the linear curves,
you might even be inclined to draw a curve like this now of course the curve
you might even be inclined to draw a curve like this.
on the drawing right now is likely an overfit and you don't want to postulate that this is the general relationship
Now of course the curve I'm drawing right now is likely an overfit. And you don't want to postulate that this is the general relationship
between the size of a house and the sales price so even though my black curve might describe Italy they're
between the size of a house and the sales price. So even though my black curve might describe the data better,
better the blue curve or the tension linear curve over here might be better explanations by virtue of Occam's razor
the blue curve or the dashed linear curve over here might be a better explanation overture of Occam's razor.
since look a little bit deeper into what we call regression as an all regression
So let's look a little bit deeper into what we call regression.
problems our data will be comprised of
As in all regression problems, our data will be comprised of
input vectors of length n that map to now a continuous value and we might be
input vectors of length in that map to another continuous value.
given a total of M data points this is
And we might be given a total of M data points.
familiar from the classification case except this time device are continuous
This is from the classification case, except this time the Ys are continuous.
once again we're looking for a function f that map's our vector X into y in linear regression
Once again, we're looking for function f that maps our vector x into y.
a function has a particular form which is w1 times X plus W 0 in the case X is
In linear regression, the function has a particular form which is W1 times X plus W0.
a one-dimensional which is N equals 1
In this case X is one dimensional which is N = 1.
well in the high dimensional space we might just write W times X plus W 0
Or in the high-dimensional space, we might just write W times X plus W0,
where W is a vector and X is a vector
where W is a vector and X is a vector.
and this is the inner product of these two vectors over here but it's for now
And this is the inner product of these 2 vectors over here.
let us consider the one-dimensional case
Let's for now just consider the one-dimensional case.
in this quiz I'm giving you the linear regression form with two unknown parameters W 1 W 0 and giving you a data
In this quiz, I've given you a linear regression form with 2 unknown parameters, W1 and W0.
set in this data set happens to be
I've given you a data set.
fillable by a linear regression model without any residual error without any
And this data set happens to be fittable by a linear regression model without any residual error.
math can you look at this and find out to me what the two parameters w0 and w1 are
Without any math, can you look at this and find out to me what the 2 parameters, W0 and W1 are?
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