1
00:00:00,200 --> 00:00:00,800
All right.

2
00:00:00,800 --> 00:00:02,866
Okay. So now I'm going to tell you
the solution.

3
00:00:02,866 --> 00:00:06,700
Well, first of course
we have to change our regressor here

4
00:00:06,700 --> 00:00:09,733
because we want to use
our polynomial regression model

5
00:00:09,733 --> 00:00:12,900
which is based on Lin rank two.

6
00:00:13,200 --> 00:00:14,466
So that's the first change.

7
00:00:14,466 --> 00:00:16,400
Lin Rick two. Yes.

8
00:00:16,400 --> 00:00:18,533
And now in the predict method,

9
00:00:18,533 --> 00:00:22,500
do you think we need to keep x
or change that by something else?

10
00:00:23,400 --> 00:00:26,833
Well of course we can't keep x
because remember x is

11
00:00:26,833 --> 00:00:30,566
only that matrix of single feature
containing the position levels.

12
00:00:30,866 --> 00:00:35,600
Remember that when we use the Lin rank
two regressor which is a linear regressor,

13
00:00:35,833 --> 00:00:39,366
it has to be applied
to the transformed matrix

14
00:00:39,366 --> 00:00:43,333
of features X into this matrix of features
at the different powers,

15
00:00:43,333 --> 00:00:47,800
you know, position level, then squared
position level, and then the other powers.

16
00:00:47,800 --> 00:00:50,066
Here we only chose n equals two so far.

17
00:00:50,066 --> 00:00:52,766
So we only have
the squared position levels.

18
00:00:52,766 --> 00:00:55,200
But that's exactly what you need to change
here.

19
00:00:55,200 --> 00:00:57,666
You can't skip X
because it is the single feature.

20
00:00:57,666 --> 00:01:02,200
So you need to input here
that transformed matrix of features

21
00:01:02,200 --> 00:01:06,000
X containing the different powers
of that single feature position level.

22
00:01:06,333 --> 00:01:10,200
And that's of course exactly this poly rig

23
00:01:10,466 --> 00:01:15,333
fit transform method apply it to this
matrix of single feature x.

24
00:01:15,566 --> 00:01:16,633
So I'm copying this.

25
00:01:16,633 --> 00:01:21,666
And that's exactly what we have
to input inside this predict method.

26
00:01:21,866 --> 00:01:22,833
You understand.

27
00:01:22,833 --> 00:01:25,733
So that was the little thing
not to forget.

28
00:01:25,733 --> 00:01:26,900
And now you're all good.

29
00:01:26,900 --> 00:01:27,533
You're ready

30
00:01:27,533 --> 00:01:31,333
to have a beautiful visualization
of the polynomial regression results.

31
00:01:31,333 --> 00:01:34,433
Let's just replace this linear here by Bo

32
00:01:34,800 --> 00:01:38,500
Li normal and now 100% ready.

33
00:01:38,600 --> 00:01:42,600
Let's visualize
the polynomial regression results.

34
00:01:42,600 --> 00:01:43,866
And there you go.

35
00:01:43,866 --> 00:01:47,866
Now we have indeed a way
more adaptive regression

36
00:01:47,866 --> 00:01:52,166
curve coming
indeed much closer to the real results.

37
00:01:52,166 --> 00:01:53,833
You know, the real salaries.

38
00:01:53,833 --> 00:01:54,366
Indeed.

39
00:01:54,366 --> 00:01:56,233
If we compare two, I'm

40
00:01:56,233 --> 00:02:00,100
going to zoom out a bit so that we can see
both of them at the same time.

41
00:02:00,100 --> 00:02:01,100
There we go.

42
00:02:01,100 --> 00:02:04,800
So if we compare these points where
we had issues previously with the linear

43
00:02:04,800 --> 00:02:09,166
regression model, well, we can clearly see
now that the issue is resolved

44
00:02:09,200 --> 00:02:12,233
because indeed the predictions
on this blue

45
00:02:12,233 --> 00:02:15,533
curve
come way closer to the real salaries.

46
00:02:15,533 --> 00:02:18,200
And this is only with n equals two.

47
00:02:18,200 --> 00:02:23,033
I'm going to show you then that with
higher powers you know n equals 3 or 4.

48
00:02:23,200 --> 00:02:25,300
Well we will get even better results.

49
00:02:25,300 --> 00:02:28,200
And I'm going to actually show this to you
right away.

50
00:02:28,200 --> 00:02:31,633
So now what we're going to do
is, well, we're going to keep this,

51
00:02:31,633 --> 00:02:35,166
but we're going to remove this
because we're going to retrain

52
00:02:35,200 --> 00:02:38,700
the polynomial regression model
with a higher degree.

53
00:02:38,800 --> 00:02:40,466
Let's take for example,

54
00:02:40,466 --> 00:02:43,466
you can try with three
but we're going to directly try with four.

55
00:02:43,500 --> 00:02:46,500
So there you go
I'm going to remove the output.

56
00:02:46,733 --> 00:02:50,066
Retrain the polynomial regression
model on the whole data set with.

57
00:02:50,066 --> 00:02:54,666
Therefore this time a degree of four,
which means that the polynomial regression

58
00:02:54,666 --> 00:03:00,600
equation will be salary equals
b0 plus b1 times position level plus

59
00:03:00,600 --> 00:03:04,766
b2 times position level square
plus B3 times position

60
00:03:04,766 --> 00:03:08,800
level of the power of three plus B4 times
position level the power of four.

61
00:03:08,866 --> 00:03:11,400
So that will be the new polynomial
regression equation.

62
00:03:11,400 --> 00:03:13,833
And so therefore let's retrain it.

63
00:03:13,833 --> 00:03:18,366
Let's build this new polynomial regression
model by just running this cell again.

64
00:03:18,733 --> 00:03:20,266
All right. So now we have it.

65
00:03:20,266 --> 00:03:23,166
And now very simply we're going
to visualize the new

66
00:03:23,166 --> 00:03:26,166
polynomial regression results
by clicking this cell here.

67
00:03:26,400 --> 00:03:29,333
And now as you can see
now the polynomial regression

68
00:03:29,333 --> 00:03:32,466
model is perfectly fitting this data set.

69
00:03:32,466 --> 00:03:34,466
So here we clearly have overfitting.

70
00:03:34,466 --> 00:03:37,466
But that's okay only in this situation
because we want to have

71
00:03:37,466 --> 00:03:43,200
a perfect prediction of the salary between
position level six and seven okay.

72
00:03:43,200 --> 00:03:45,133
And now one final thing
because I really want you

73
00:03:45,133 --> 00:03:48,000
to have the best results
and best visualizations.

74
00:03:48,000 --> 00:03:48,333
Indeed.

75
00:03:48,333 --> 00:03:52,200
As you can see here, what happened
is that only some straight lines

76
00:03:52,200 --> 00:03:57,633
where plotted between each
consecutive points of the data set, right?

77
00:03:57,900 --> 00:04:01,900
And therefore that makes this curve
not as smooth as we would hope for.

78
00:04:02,266 --> 00:04:06,233
So I actually prepared another code,
but which we won't code together,

79
00:04:06,233 --> 00:04:09,300
because this is just for the sake
of having a more beautiful curve.

80
00:04:09,466 --> 00:04:12,966
So we're going to get it
from the original implementation.

81
00:04:13,400 --> 00:04:14,966
It is actually right here.

82
00:04:14,966 --> 00:04:16,733
You see visualizing the polynomial

83
00:04:16,733 --> 00:04:19,733
regression results for higher resolution
and smoother curve.

84
00:04:19,733 --> 00:04:23,733
So I'm going to take all this code
and then paste it

85
00:04:24,066 --> 00:04:28,100
in our copy of the implementation
right here.

86
00:04:28,100 --> 00:04:29,400
And your code cell.

87
00:04:29,400 --> 00:04:30,500
And you will see that

88
00:04:30,500 --> 00:04:34,500
we will get indeed a much smoother
and more beautiful curve as you can see.

89
00:04:34,500 --> 00:04:35,166
Right.

90
00:04:35,166 --> 00:04:38,400
And the trick to plot this curve,
I'm going to explain this quickly

91
00:04:38,866 --> 00:04:42,600
is just to, instead of taking
you know, the integers zero, one,

92
00:04:42,600 --> 00:04:44,833
two, three, four, five, six, seven, eight,
nine, ten.

93
00:04:44,833 --> 00:04:47,800
Well, we increase
the density of these points by taking

94
00:04:47,800 --> 00:04:52,666
not only these integers, but,
you know, 11.1, 1.2, 1.3, and 1.4

95
00:04:52,900 --> 00:04:56,833
up to, you know, 9.1, 9.2, 9.8, 9.9, ten.

96
00:04:56,833 --> 00:04:58,666
That's what this 0.1 means.

97
00:04:58,666 --> 00:05:00,466
That's what we call this tip.

98
00:05:00,466 --> 00:05:02,700
All right.
So you don't have to understand this.

99
00:05:02,700 --> 00:05:03,600
You can if you want.

100
00:05:03,600 --> 00:05:07,300
But this is something you will probably do
only once in your life, because I remind

101
00:05:07,300 --> 00:05:10,300
that usually your data sets
will have many features.

102
00:05:10,300 --> 00:05:14,233
And here I only took one feature in order
to show you the results on a graph.

103
00:05:14,333 --> 00:05:16,466
Because, you know,
if we had many features, I couldn't

104
00:05:16,466 --> 00:05:19,400
show this to you because we would have way
too many dimensions.

105
00:05:19,400 --> 00:05:21,600
So don't worry too much about this, okay?

106
00:05:21,600 --> 00:05:23,666
But just appreciate the result, right?

107
00:05:23,666 --> 00:05:25,366
We have a very well trained

108
00:05:25,366 --> 00:05:29,433
and therefore very well fitted
but overfitted model for this data set.

109
00:05:29,633 --> 00:05:33,600
But that's fine because then indeed
we will be able to get an amazing

110
00:05:33,600 --> 00:05:38,000
and accurate prediction
to figure out if there is truth or.