1
00:00:00,066 --> 00:00:01,033
So let's do this.

2
00:00:01,033 --> 00:00:03,900
Let's close the linear regression results.

3
00:00:03,900 --> 00:00:07,566
And let's start to visualize
the polynomial regression results.

4
00:00:07,933 --> 00:00:11,933
And you're going to see now
how easy it is to go from the linear

5
00:00:11,933 --> 00:00:14,933
regression results
to the polynomial regression results.

6
00:00:14,933 --> 00:00:17,733
Because what we will simply do here is,

7
00:00:17,733 --> 00:00:21,600
you know, select this and paste it here.

8
00:00:21,966 --> 00:00:25,100
And now you will see how
we only need to change very few things.

9
00:00:25,433 --> 00:00:27,400
So as usual let's start with the simplest.

10
00:00:27,400 --> 00:00:30,900
Let's replace linear here by polynomial

11
00:00:32,766 --> 00:00:33,500
okay.

12
00:00:33,500 --> 00:00:34,866
And now what do we need to change.

13
00:00:34,866 --> 00:00:35,200
Okay.

14
00:00:35,200 --> 00:00:38,366
So do we need to change something
in the June point function.

15
00:00:38,400 --> 00:00:42,100
No of course because we want to keep
the same real observations.

16
00:00:42,266 --> 00:00:43,600
So that's okay.

17
00:00:43,600 --> 00:00:46,600
And then do we need to change something
in the germline function.

18
00:00:46,800 --> 00:00:48,066
Of course. Yes.

19
00:00:48,066 --> 00:00:51,833
Because here we are
predicting the salaries of our

20
00:00:51,833 --> 00:00:55,700
ten levels in our data set
according to our linear regression model.

21
00:00:56,100 --> 00:00:58,600
So according to you
what do we need to change here.

22
00:00:58,600 --> 00:00:59,533
Very simply.

23
00:00:59,533 --> 00:01:03,700
Well actually we just need to change
the regressor in the predict function.

24
00:01:04,066 --> 00:01:07,533
And instead of taking the line drag,
which is the linear regressor,

25
00:01:07,800 --> 00:01:12,233
we're going to take the polynomial
regressor that we called poly rank.

26
00:01:12,600 --> 00:01:13,566
And that's it.

27
00:01:13,566 --> 00:01:16,300
That's actually all we need to do
to visualize

28
00:01:16,300 --> 00:01:18,000
the polynomial regression results.

29
00:01:18,000 --> 00:01:21,200
And you will see that in the next sections
it will actually be the same.

30
00:01:21,200 --> 00:01:24,333
We will only need to change the regressor
to plot

31
00:01:24,333 --> 00:01:27,933
the new graphic results
of our future regressors.

32
00:01:28,433 --> 00:01:29,733
So that's very nice.

33
00:01:29,733 --> 00:01:33,000
We're actually ready right now
to visualize the polynomial results.

34
00:01:33,200 --> 00:01:35,066
So let's do this with our waiting.

35
00:01:35,066 --> 00:01:39,133
I'm going to select this
and press Command and Control.

36
00:01:39,133 --> 00:01:40,266
Press enter to execute.

37
00:01:42,033 --> 00:01:43,200
And here it is.

38
00:01:43,200 --> 00:01:46,433
As you can see this is not a straight line
anymore.

39
00:01:46,833 --> 00:01:49,500
Let's zoom on the graph.

40
00:01:49,500 --> 00:01:50,000
All right.

41
00:01:50,000 --> 00:01:53,366
So as I just mentioned, the first reflex
to have as a machine learning

42
00:01:53,366 --> 00:01:57,466
scientists is that, 
this is not a linear model anymore.

43
00:01:57,466 --> 00:01:59,400
And by the way, congratulations.

44
00:01:59,400 --> 00:02:02,700
You just made your very first non-linear
model.

45
00:02:03,333 --> 00:02:06,533
We're going to see plenty of other
non-linear models in this course.

46
00:02:06,766 --> 00:02:08,166
But this is your first one.

47
00:02:08,166 --> 00:02:09,933
So congratulations.

48
00:02:09,933 --> 00:02:12,266
So as you can see
it's not a straight line.

49
00:02:12,266 --> 00:02:13,433
Now it's a curve.

50
00:02:13,433 --> 00:02:18,833
And we can immediately see that
the curve is approaching much better.

51
00:02:18,833 --> 00:02:21,166
All the red observation points.

52
00:02:21,166 --> 00:02:24,433
And especially for the CEO here,
the CEO wouldn't get mad

53
00:02:24,433 --> 00:02:28,333
now if we negotiated with him
its future salary in a new company,

54
00:02:28,566 --> 00:02:32,166
because now the prediction is much closer
to the realization point.

55
00:02:32,666 --> 00:02:38,700
And let's check our employee that is about
to be hired and that has a 6.5 level.

56
00:02:39,100 --> 00:02:42,100
Well, 6.5 is around here.

57
00:02:42,166 --> 00:02:45,566
And when we project 6.5
on our polynomial regression

58
00:02:45,566 --> 00:02:50,900
model represented by this blue curve, here
we get a predicted salary.

59
00:02:50,900 --> 00:02:55,466
Here I'm projecting the point on the curve
back again on the salary axis.

60
00:02:55,666 --> 00:02:59,400
And we get actually a salary
that is coming much closer

61
00:02:59,400 --> 00:03:04,833
to the salary mentioned by this future
employee, which is around 160 K here.

62
00:03:04,833 --> 00:03:07,233
Well,
we don't get the accurate prediction yet

63
00:03:07,233 --> 00:03:09,866
because that's what we were going to do
in the next tutorial.

64
00:03:09,866 --> 00:03:13,533
But definitely
this model is fitting much better.

65
00:03:13,566 --> 00:03:14,433
The data set.

66
00:03:14,433 --> 00:03:15,433
And now, just for fun,

67
00:03:15,433 --> 00:03:19,266
let's add a new degree to see
how this model can still be much improved

68
00:03:19,266 --> 00:03:24,166
and almost passing by all the points
very accurately as we add more degrees.

69
00:03:24,500 --> 00:03:25,300
So let's check it out.

70
00:03:25,300 --> 00:03:28,033
Let's close
this and let's add a new degree.

71
00:03:28,033 --> 00:03:30,300
So very simply what we're going to do

72
00:03:30,300 --> 00:03:34,066
is add a new degree
here by copying this line.

73
00:03:35,166 --> 00:03:36,400
Paste it here.

74
00:03:36,400 --> 00:03:40,666
And we're going to add a new column
in our data set level four that will

75
00:03:40,666 --> 00:03:44,866
correspond to our original independent
variable level at the power four.

76
00:03:45,233 --> 00:03:48,666
And so therefore here
we need to compute it this way

77
00:03:48,666 --> 00:03:52,233
by taking the fourth
power of level there.

78
00:03:52,700 --> 00:03:58,600
And now let's execute this line to add
the level four column in our data set.

79
00:03:58,633 --> 00:04:00,666
Now you can check to see that it's here
level four.

80
00:04:00,666 --> 00:04:01,633
Perfect.

81
00:04:01,633 --> 00:04:05,666
And now let's reselect this
to rebuild our new polynomial regression

82
00:04:05,666 --> 00:04:07,700
model with this fourth degree. Now.

83
00:04:07,700 --> 00:04:11,633
So executing a new polynomial regression
model created.

84
00:04:11,866 --> 00:04:13,833
And now let's have a look at the results.

85
00:04:13,833 --> 00:04:15,300
So these are the previous results

86
00:04:15,300 --> 00:04:19,066
corresponding to a polynomial regression
model with a third degree.

87
00:04:19,066 --> 00:04:21,833
And now let's look at what happens
with the fourth degree.

88
00:04:21,833 --> 00:04:24,966
So I'm going to select this and execute.

89
00:04:24,966 --> 00:04:28,300
And here are the polynomial regression
results

90
00:04:28,300 --> 00:04:32,700
for a polynomial regression model
with a fourth degree okay.

91
00:04:32,700 --> 00:04:35,533
So as you can see we can zoom on it
if you want.

92
00:04:35,533 --> 00:04:36,300
As you can see

93
00:04:36,300 --> 00:04:40,133
the line is actually strictly passing
by all the red observation points.

94
00:04:40,366 --> 00:04:43,766
And now the CEO would be even happier
with the negotiation

95
00:04:43,766 --> 00:04:47,166
or should I say even less furious
because the prediction

96
00:04:47,166 --> 00:04:50,833
now is actually almost
the same as a real observation point.

97
00:04:50,900 --> 00:04:55,733
That is, the predicted salary is almost
the same as the real salary.

98
00:04:56,633 --> 00:05:00,733
Okay, and same for our 6.5 level employee.

99
00:05:01,133 --> 00:05:05,166
When we project this 6.5 level
here on the curve and then projected again

100
00:05:05,166 --> 00:05:09,233
on the Y axis, that is the salary axis,
we get a value around what he said.

101
00:05:09,233 --> 00:05:11,100
That is 160 K.

102
00:05:11,100 --> 00:05:12,400
And for those of you who are interested

103
00:05:12,400 --> 00:05:15,400
in having a more continuous curve here,
like we did in Python,

104
00:05:15,400 --> 00:05:19,033
I will add the code for that job
in the R file provided in this section.

105
00:05:19,200 --> 00:05:20,400
You can check it out for fun.

106
00:05:20,400 --> 00:05:24,533
And this is the model we're going to use
to get the accurate prediction

107
00:05:24,533 --> 00:05:26,433
of the previous salary
of this new employee

108
00:05:26,433 --> 00:05:27,900
that is about to be hired,

109
00:05:27,900 --> 00:05:30,833
and we will compare it to the salary
that it pretended

110
00:05:30,833 --> 00:05:32,866
to have in its previous company

111
00:05:32,866 --> 00:05:36,933
and eventually tell our final verdict
whether it's truth or bluff.

112
00:05:37,500 --> 00:05:40,066
So I look forward to doing that with you
in the next tutorial.

113
00:05:40,066 --> 00:05:41,866
And until then, enjoy machine learning.