Geography Reference
In-Depth Information
Table 3.3
Variable 1 (
y
) and variable 2 (
z
), squared
differences from their mean, and summed values.
i
yy
2
(
)
(
i
zz
-
)
2
Variable 1 (
y
i
)
Variable 2 (
z
i
)
12
6
404.46
729.00
34
52
3.57
361.00
32
41
0.01
64.00
12
25
404.46
64.00
11
22
445.68
121.00
14
9
328.01
576.00
56
43
570.68
100.00
75
67
1839.46
1156.00
43
32
118.57
1.00
Sum
4114.89
3172.00
and its mean multiplied by the square root of the sum of squared dif erences between
z
and its mean. h ese two sets of products are then multiplied together.
We have already seen the dif erences between
y
and
z
and their respective means in
Table 3.2. h e squared dif erences and their sums are given in Table 3.3 (note that the
values in column 3 are the same as those in the i nal column of Table 3.2).
Given the values in Table 3.3, the numerator is obtained from:
n
Â
1
(
yyzz
-
)(
-
)
=
3092
(as calculated above)
i
i
i
=
and the denominator is obtained from:
Â
n
Â
n
(
yy
-
)
2
(
zz
-
)
2
=
4114.89 3172.00
64.1474 56.3205
3612.8136
¥
i
i
i
=
1
i
=
1
=
¥
=
h e correlation coei cient is then given by:
3092
r
=
=
0.8558
3612.8136
h e
r
value is positive and indicates, as the slope value, that the variables are positively
related: as the value in one variable increases so does the value of the other. If the
r
value
was negative, this would indicate negative correlation: as the value in one variable
decreased, the value of the other would increase. Possible values of
r
range from -1
(indicating perfect negative correlation) to +1 (indicating perfect positive correlation).
h e coei cient of determination is ot en used to indicate the goodness of i t, which
is simply the squared correlation coei cient and is given by
r
2
. In our example (given
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