This preview shows pages 1–3. Sign up to view the full content.
1
Introduction to Business Statistics
L
e
c
t
u
r
e
2
3
Correlation Analysis
Correlation coefficient:
It measures the strength of the relationship
between independent variable
X
and dependent variable
Y
.
SSY
SSX
SSXY
S
Y
Y
S
X
X
n
r
Y
i
n
i
X
i
=
−
−
−
=
∑
=
)
(
)
(
1
1
1
z
1
1
≤
≤
−
r
z
Positive (negative)
r
indicates a positive (negative) association:
Increasing
X
tends to increase (decrease)
Y
.
z
1
=
r
or
1
−
=
r
occur only in the case of perfect linear association.
z
The value of
r
does not change when the unit of measurement of
X
or
Y
or both are changed.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document 2
z
r
measures only the strength of linear relationship between two
variables.
z
The leastsquare slope estimate
1
b
can be calculated from
r
via
X
Y
S
S
r
b
=
1
, where
Y
X
S
S
,
is the sample s.d. for
X
and
Y
, respectively.
z
The preceding equation implies that
Y
X
rS
b
S
=
1
, indicating that a
change of one standard deviation in
X
corresponds to a change of
r
standard deviations in
Y
.
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 02/13/2012 for the course ISOM 111 taught by Professor Hu,inchi during the Fall '10 term at HKUST.
 Fall '10
 Hu,Inchi

Click to edit the document details