How to program the Best Fit Line - Practical Machine Learning Tutorial

what is going on everybody welcome to
part 9 of our machine learning tutorial
series in this tutorial we are going to
be continuing working on linear
regression here and what we're going to
be doing is we've got the slope now we
need to calculate the y-intercepts
and just as a reminder the reason why
we're doing this is this is the
calculation for the slope of the best
fit line and now we need to do the
calculation for the y-intercept of the
best fit line as a reminder the
calculation of the y-intercept for the
best fit line is B which is the
y-intercept equals the mean of the Y's
minus M times the mean of the X so
actually this equation is probably is in
theory the most complex equation because
it includes the calculation of M but
once you have M this one's actually
pretty darn easy so this will be pretty
quick so so the first thing we're going
to go ahead and do is no longer is this
function only best fit slope its best
fit slope and intercept great so M
equals the following and then we need to
also return B so then M B and then M be
great ok now we actually need to have be
somewhere in this function well that's
pretty simple because it's just B equals
the mean of the Y's right so let's go
back to the function me otherwise minus
M times the mean of the X's so me
otherwise minus M and times the mean of
the X's so so that's our B and now we
can return M and B so we can go ahead
and print that up we didn't change the
name of the function what a newb ok so
there we go we've got our best fit slope
and the best fit
y intercepts
so now what if we wanted to actually
create a line that fits the data that
we've got here well it's really simple
because we have the calculation right
we've got MMB so now we just need to
make like a list of Y's so for example
we could say regression underscore line
equals and in this case it would be
remember y equals MX plus B so this
would be we could make a one line for
loop pretty much here so we do M times X
what a mess up okay mm times X plus B so
that's it's MX plus B for X in X's okay
so we would just use the same axes here
1 2 3 4 5 6 and basically we're just
saying MX plus B for each X in X so this
is just a one line for loop that will
create this regression line for us this
is exactly identical as doing like for X
in X's regression line dot append this
ok
just for the record anyway that's our
regression line okay so we've already
got matplotlib belt-high plot let's go
ahead and from matplotlib import style
because now that we've made something
cool we want to use style 538 okay we've
got a regression line now we're going to
do PLT dots scatter X is wise and then
PLT dot plot X is regression line and
then finally we're going to appeal to -
Oh boom
regression line ok and that looks pretty
good to me
it probably hopefully looks pretty good
to you so close that and what if what if
so we've got this data here let me pull
it back up actually we've got our data
and what if now remember you're like you
might be thinking well great you've
created a regression line what does that
mean to me but the whole point is that
you can now at this point you first of
all you've created a model for the for
the data right y equals MX plus B where
m is equal to 0.42 and B is 4 that is
the model of our data and so using that
model we can find out other information
we could make a prediction if we wanted
so for example we could say let's say
predict underscore x equals 8 so we want
to predict y where x equals 8 well
that's pretty easy predicts y equals it
would just be M times predict X so MX
plus B right simple enough and then we
can even I'm trying to think if I want
to scatter it I guess yeah coming
because that's a prediction so PLC how
is scatter and then we'll just I'm just
going to copy this copy and paste and
change that and then now if we were to
bring this up this is our prediction and
in fact we could scatter and then we're
going to make we'll do color equals G
for green ok so our prediction isn't
even see like yeah it would go all the
way to that little little spot there ok
so um so now we're at the point where we
were able to we had some data we fit a
model to that data and we even learned
how to make a prediction based on that
data are we done well we've got what we
need to make predictions but there's
another integral part of all of this and
that is remember before um where we said
ok we don't want just a good line we
want the best line by the same token not
only do we want the best fit line we
want that best fit line to be a good fit
line right you want it to be a good fit
in this case it's a good fit but we can
find the best fit line to a very poor
of data and the question is how good is
this best fit line and maybe more more
accurately put how accurate is the best
fit line so we can actually calculate
how good of a fit this best fit line is
and when you do that you've got a model
and the model might have a prediction
right and the prediction might have a
certain accuracy to it but it also might
have a certain confidence to it as well
and linear regression accuracy and
confidence are very similar until you
start getting into many many many
dimensions but then when we get into
something like K nearest neighbors you
can definitely have a very big
difference between accuracy and
confidence but anyways the next step
that we need to do is figure out how
good of a fit is the best fit line and
that's what we're going to be talking
about in the next tutorial you have any
questions or comments leave them below
otherwise until next time