1
00:00:00,166 --> 00:00:03,633
In this tutorial we will be talking about
false positives and false negatives.

2
00:00:04,033 --> 00:00:07,666
As you remember where we were using
the logistic regression

3
00:00:07,666 --> 00:00:12,566
function to observe where for random

4
00:00:12,766 --> 00:00:17,700
values of the independent variable
will end up in terms of y hat.

5
00:00:17,700 --> 00:00:21,633
So in terms of the predicted value
for the dependent variable,

6
00:00:22,000 --> 00:00:25,500
and we agreed that anything below
the 50% line

7
00:00:26,033 --> 00:00:33,300
will be projected downwards onto the zero
horizontal line, and anything above

8
00:00:33,300 --> 00:00:39,300
the 50% line will be projected
upwards onto the 100% horizontal line.

9
00:00:40,000 --> 00:00:45,000
And that allowed us to turn probabilities
into actual predictions.

10
00:00:45,000 --> 00:00:48,000
So either yes or no.

11
00:00:48,600 --> 00:00:50,133
Now let's take a step back.

12
00:00:50,133 --> 00:00:53,333
Where did we get these four values from?

13
00:00:53,566 --> 00:00:57,400
So we took four random values
of the independent variable.

14
00:00:57,833 --> 00:01:00,833
And we just had a look at
what would happen to them.

15
00:01:00,966 --> 00:01:04,633
How we can use how we would use
the logistic regression function

16
00:01:04,800 --> 00:01:07,733
to ascertain what's probability

17
00:01:07,733 --> 00:01:11,066
they have and what y hat values they have.

18
00:01:11,066 --> 00:01:14,866
So how about we take another step back
and we forget

19
00:01:14,866 --> 00:01:16,800
about these four random values.

20
00:01:16,800 --> 00:01:19,033
And instead of taking four random values

21
00:01:19,033 --> 00:01:22,766
of the independent variable,
how about we take four known values.

22
00:01:22,800 --> 00:01:27,866
In fact, let's take four values for the
independent variable from our data set.

23
00:01:27,900 --> 00:01:32,800
So let's just pick out four values that
we really know that exist in our data set.

24
00:01:32,800 --> 00:01:37,066
And we use them to create
this logistic regression.

25
00:01:38,266 --> 00:01:40,200
And let's do the same thing with them.

26
00:01:40,200 --> 00:01:43,866
Let's see where they will end up
if we apply the model to them.

27
00:01:44,133 --> 00:01:48,400
And as you can see here,
the label of the vertical axis change to Y

28
00:01:48,533 --> 00:01:52,400
because this is the
we already know that in red is the actual

29
00:01:52,666 --> 00:01:56,400
value of the dependent variable,
because we know the result, those,

30
00:01:56,766 --> 00:01:58,300
the people on the bottom.

31
00:01:58,300 --> 00:02:01,666
So observations number one and number
three, they didn't take up the offer

32
00:02:01,666 --> 00:02:04,666
the email offer and the observations.

33
00:02:04,733 --> 00:02:09,933
on the top, people number two and four,
they did take up the email offer.

34
00:02:09,933 --> 00:02:12,700
So let's see what happens to them

35
00:02:12,700 --> 00:02:15,700
if we apply our logistic regression model.

36
00:02:16,500 --> 00:02:19,300
So step number one would be to project

37
00:02:19,300 --> 00:02:22,300
these values onto the curve.

38
00:02:22,833 --> 00:02:23,633
Makes sense right.

39
00:02:23,633 --> 00:02:26,366
So we just want to see
where they end up on the curve.

40
00:02:26,366 --> 00:02:28,366
That's our blue dots over there.

41
00:02:28,366 --> 00:02:32,366
That's where they have been modeled
by the curve.

42
00:02:33,000 --> 00:02:36,166
Now we can from here
we can say what the probabilities are.

43
00:02:36,166 --> 00:02:37,600
You just have to project to the left.

44
00:02:37,600 --> 00:02:41,300
And you can see approximately
that for observation number one,

45
00:02:41,766 --> 00:02:46,866
it's, about maybe 20%, ten, 15%,
maybe let's say 15%.

46
00:02:46,866 --> 00:02:50,933
Observation number two,
it's about 40% observation number three,

47
00:02:51,066 --> 00:02:54,933
I would say about 70% observation
and before about 85%.

48
00:02:55,666 --> 00:02:59,233
But we're not interested in probabilities
per se right now.

49
00:02:59,233 --> 00:03:03,133
What we want to get to
is the actual y hat.

50
00:03:03,133 --> 00:03:05,100
We want to see what the predicted
value will be.

51
00:03:05,100 --> 00:03:08,233
So we want to say 
we want to see if the model will tell us,

52
00:03:08,566 --> 00:03:11,900
are these people, 
going to take up the offer or not?

53
00:03:11,900 --> 00:03:15,766
And why do we want to do this is because
we already know the result, right?

54
00:03:15,766 --> 00:03:19,200
We already know what the result
will be, or was.

55
00:03:19,533 --> 00:03:22,900
And we just want to see
we want to kind of, assess the model.

56
00:03:22,900 --> 00:03:24,800
We want to see how well it's working.

57
00:03:24,800 --> 00:03:27,000
And, if it's going to make any mistakes.

58
00:03:27,966 --> 00:03:28,600
So let's go

59
00:03:28,600 --> 00:03:32,366
ahead and proceed with our logic
for getting the y hat.

60
00:03:32,566 --> 00:03:33,866
And what was the logic there?

61
00:03:33,866 --> 00:03:37,300
Well, the same thing that we discussed
just a few minutes ago

62
00:03:37,300 --> 00:03:38,600
at the start of this tutorial.

63
00:03:38,600 --> 00:03:42,400
Anything we're using this arbitrary
horizontal line 50%.

64
00:03:42,400 --> 00:03:45,766
So anything below
this line is going to be projected

65
00:03:45,900 --> 00:03:49,366
onto the horizontal line, which is zero.

66
00:03:49,366 --> 00:03:53,766
So where we're saying that the offer
is not going to be taken up

67
00:03:54,300 --> 00:03:57,166
and anything above the 50%
line will be projected

68
00:03:57,166 --> 00:04:02,100
onto the horizontal line, which is 1
or 100%, where we're saying that

69
00:04:02,533 --> 00:04:06,700
those people that end up on that line
are definitely going to take up the offer.

70
00:04:07,300 --> 00:04:10,300
So let's go ahead and do that.

71
00:04:10,333 --> 00:04:11,500
There we go. In gray.

72
00:04:11,500 --> 00:04:15,200
We have our projections
or our predicted value.

73
00:04:15,200 --> 00:04:17,366
So y hat is in gray.

74
00:04:17,366 --> 00:04:21,300
And it's very interesting to see both y
and y hat on one chart.

75
00:04:21,300 --> 00:04:23,733
So that means what actually happened
is in red.

76
00:04:23,733 --> 00:04:26,733
And what we predicted was going to happen
is in gray.

77
00:04:27,000 --> 00:04:30,666
And right away you can see that for
observations number one and number four.

78
00:04:30,666 --> 00:04:34,800
So for those people in observation

79
00:04:34,800 --> 00:04:37,900
number one, number four they
we predicted correctly.

80
00:04:37,900 --> 00:04:42,000
So we said for the person number one,
we predicted that

81
00:04:42,166 --> 00:04:43,633
he won't take up the offer.

82
00:04:43,633 --> 00:04:48,200
And he actually did not take up the offer
because the red,

83
00:04:48,200 --> 00:04:51,200
mark is also on the same horizontal line.

84
00:04:51,200 --> 00:04:53,666
Now for observation number four,
same thing.

85
00:04:53,666 --> 00:04:54,666
We predicted that

86
00:04:54,666 --> 00:04:58,500
that person will take up the offer,
and they did take up the offer.

87
00:04:58,966 --> 00:04:59,800
That's good.

88
00:04:59,800 --> 00:05:02,033
But now let's have a look at observation
number two.

89
00:05:02,033 --> 00:05:03,733
And number three you can see that

90
00:05:04,766 --> 00:05:07,800
for observation
number two the gray lines at the bottom,

91
00:05:08,100 --> 00:05:10,900
the gray marks at the bottom, meaning that

92
00:05:10,900 --> 00:05:15,600
the model is predicting for this person
based on their gender, based on their age.

93
00:05:15,600 --> 00:05:18,933
Well, in this case, just age,
because we're doing a single,

94
00:05:19,333 --> 00:05:21,766
variable logistic regression.

95
00:05:21,766 --> 00:05:25,900
So based on their age,
this model is saying that this person

96
00:05:25,900 --> 00:05:30,033
is not going to take up the offer
because the gray mark is at the bottom.

97
00:05:30,300 --> 00:05:33,200
However, we can see that
the red mark is at the top,

98
00:05:33,200 --> 00:05:37,166
meaning that this person
did take up the offer and that means

99
00:05:37,166 --> 00:05:40,166
that the logistic regression
made an error here.

100
00:05:40,366 --> 00:05:43,366
And same thing for person number three.

101
00:05:44,000 --> 00:05:46,200
The gray mark is at the top.

102
00:05:46,200 --> 00:05:49,500
And that means that the model
is predicting that the person will

103
00:05:49,500 --> 00:05:50,600
will take up the offer.

104
00:05:50,600 --> 00:05:53,900
But the red marks at the bottom,
meaning that the person didn't actually

105
00:05:53,900 --> 00:05:57,900
take up the offer and therefore
the logistic regression made a mistake.

106
00:05:57,900 --> 00:05:59,400
Once again.

107
00:05:59,400 --> 00:06:02,866
And these mistakes,
they actually have specific names.

108
00:06:02,866 --> 00:06:08,900
So the top mistake over there is a false
positive or a type one error.

109
00:06:09,066 --> 00:06:10,800
What does false positive mean.

110
00:06:10,800 --> 00:06:15,266
Well it means that we said
we predicted a positive outcome.

111
00:06:15,266 --> 00:06:16,233
But it was false.

112
00:06:16,233 --> 00:06:20,433
So we were
we predicted an effect that did not occur.

113
00:06:21,233 --> 00:06:25,500
And the other mistake you see
here has a different name.

114
00:06:25,500 --> 00:06:28,300
It's called a false negative.
So we predicted that

115
00:06:28,300 --> 00:06:30,300
there won't be an effect.

116
00:06:30,300 --> 00:06:32,100
But the effect actually did occur.

117
00:06:32,100 --> 00:06:36,266
So our prediction was negative
meaning there won't be an effect.

118
00:06:36,266 --> 00:06:37,633
But it was a false negative.

119
00:06:37,633 --> 00:06:39,900
And it's called a type two type of error.

120
00:06:39,900 --> 00:06:42,600
And the way I personally remember them,

121
00:06:42,600 --> 00:06:45,500
it's important
also to distinguish between the two.

122
00:06:45,500 --> 00:06:49,800
The way I personally remember them is,
I think of type

123
00:06:49,800 --> 00:06:53,866
one as less dangerous than type two.

124
00:06:53,866 --> 00:06:59,700
So type type one is less, for me
in my in my mind, although it's not

125
00:06:59,700 --> 00:07:02,700
necessarily the case, but the way
that's the way I remember them.

126
00:07:02,700 --> 00:07:05,133
That type one is kind of like a warning.

127
00:07:05,133 --> 00:07:07,566
So that's why
there's an orange explanation, Mark.

128
00:07:07,566 --> 00:07:09,600
And it's, it's a false positive.

129
00:07:09,600 --> 00:07:12,600
So basically you said something
is going to happen, but it didn't happen.

130
00:07:12,600 --> 00:07:14,166
So you said
maybe there'll be an earthquake,

131
00:07:14,166 --> 00:07:15,266
but there wasn't an earthquake.

132
00:07:15,266 --> 00:07:17,566
So, you know,
that's not the end of the world.

133
00:07:17,566 --> 00:07:22,266
But false negative is a bit worse
in my once again understanding because,

134
00:07:22,833 --> 00:07:25,033
once if you say something,
it's not going to happen,

135
00:07:25,033 --> 00:07:27,800
but it actually does happen,
then you can't even be prepared for it.

136
00:07:28,966 --> 00:07:32,466
And that's
why type two is, false negative.

137
00:07:32,466 --> 00:07:34,566
And that's how I remember them personally.

138
00:07:34,566 --> 00:07:37,500
But once again, it could be absolutely.

139
00:07:37,500 --> 00:07:41,366
they can both be pretty serious errors,
especially when you are dealing

140
00:07:41,366 --> 00:07:44,366
with, like medical conclusions
and stuff like that.

141
00:07:44,433 --> 00:07:47,900
So those are false
positives and false negatives.

142
00:07:48,566 --> 00:07:51,466
we will be using them more
when we talk about

143
00:07:51,466 --> 00:07:54,466
the confusion matrix in the next tutorial.

144
00:07:54,600 --> 00:07:55,833
And I look forward to see you next time.

145
00:07:55,833 --> 00:07:58,833
Until then, happy analyzing.