Database Reference
In-Depth Information
Lift
10
8
6
4
2
Deciles
12345 6789
Fig. 4.5
A typical lift chart.
coecient. This measure can be used to find the correlation between the
ordered estimated conditional probability (
p
[
k
]
) and the ordered actual
expected outcome (
t
[
k
]
). A Pearson correlation coecient can have any
value between
1 and 1 where the value 1 represents the strongest positive
correlation. It should be noticed that this measure take into account not
only the ordinal place of an instance but also its value (i.e. the estimated
probability attached to it). The
Pearson
correlation coecient for two
random variables is calculated by dividing the co-variance by the product
of both standard deviations. In this case, the standard deviations of the
twovariablesassumingaquotasizeof
j
are:
−
j
j
p
[
i
]
−
p
(
j
)
;
t
[
i
]
−
t
(
j
)
,
1
j
1
j
σ
p
(
j
)=
σ
t
(
j
)=
(4.14)
i
=1
i
=1
where
p
(
j
)
, t
(
j
) represent the average of
p
[
i
]
's and
t
[
i
]
's respectively:
j
j
p
[
i
]
t
[
i
]
i
=1
t
(
j
)=
i
=1
p
(
j
)=
;
=
Hit
-
Rate
(
j
)
.
(4.15)
j
j
The co-variance is calculated as follows:
j
p
[
i
]
−
p
(
j
)
(
t
[
i
]
−
Cov
p,t
(
j
)=
1
j
t
(
j
))
.
(4.16)
i−
1
Thus, the Pearson correlation coecient for a quota
j
,is:
Cov
p,t
(
j
)
σ
p
(
j
)
ρ
p,t
(
j
)=
σ
t
(
j
)
.
(4.17)
·
Search WWH ::
Custom Search