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Now that we've defined a notation, let's
go back to a decision boundary example and

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look at the impact of those
coefficients that we've learned on

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the actual decision boundary
that we've obtained.

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So in the example that we had,

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the score was defined by 1.0
times awesome- 1.5 times awful.

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That means that, W1 was 1.0,
W2 was -1.5, and here, W0 was 0.

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I didn't show that 0 there,
it was kind of saying that 0 is 0.

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And that's how we got a decision boundary,
where the score below the line

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was greater than 0 and the score above
the line was less than 0 and that's

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what made the predictions be positive
on one side, negative on the other.

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Now, lets say that instead I had learned
that the coefficient W0 was 1.0,

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instead of 0.

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What does that mean?

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That means that our Score
function now has this extra term,

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1.0 times + 1.0 times
awesome- 1.5 times awful.

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So what happens to the line
to that decision boundary?

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Well, that line gets shifted up.

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And so if you look at that point on
the lower left, which is close to 0.0,

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which before we predicted
as being a negative review.

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After we make that change, we now
predict it to be a positive review, so

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it turns from orange to blue.

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On the other hand, if you take the
coefficient awful, which is now -1.5, and

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we increase it, we say it's -3.0,
so awfuls are just really awful.

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What happens to our equation?

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Well, the -1.5 gets replaced by -3.0, so

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it becomes 1.0 + 1.0#awesomes,-
3 times #awfuls.

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And that curve tilts down a little bit.

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So if you look at that new point that
was on the positive prediction side,

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it gets shifted to the other side of the
decision boundary and it turns from blue

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to orange and that's because you have two
awfuls in it and awfuls are just awfuls.

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And before they were counter balanced by
the four awesomes in that data point,

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but now the four awesomes can't
counter balance the two awfuls.

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