HP 12C#ABA hp 12c_solutions handbook_English_E.pdf - Page 118

Covariance, Example

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3. Repeat step 2 for each new case. Example: Find Q(x) for x = 1.18 and x = 2.1. Keystrokes Display 1.18 0.12 Q(1.18) 2.1 0.02 Q(2.1) Covariance Covariance is a measure of the interdependence between paired variables (x and y). Like standard deviation, covariance may be defined for either a sample (Sxy) or a population (S'xy) as follows: Sxy = r * sx * sy S'xy = r * s'x * s'y The following procedure finds the covariance of a sample (Sxy) and of a population (S'xy): 1. Press CLEAR . 2. Key in the y-values and press 3. Key in the x-values and press pairs. . . Repeat steps 2 and 3 for all data 4. Press to obtain the value of Sxy. 5. Press 1 1 1 to obtain S'xy. Example 1: Find the sample covariance (Sxy) and population covariance (S'xy) for the following paired variables: xi 26 30 44 50 62 68 74 yi 92 85 78 81 54 51 40 Keystrokes Display CLEAR 92 26 85 30 7.00 Total number of entries. 78 44 81 50 117

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117
3.
Repeat step 2 for each new case.
Example:
Find
Q
(
x
) for
x
= 1.18 and
x
= 2.1.
Covariance
Covariance is a measure of the interdependence between paired
variables (
x
and
y
). Like standard deviation, covariance may be defined
for either a sample (S
xy
) or a population (S'
xy
) as follows:
S
xy
=
r
*
s
x
*
s
y
S'
xy
=
r
*
s'
x
*
s'
y
The following procedure finds the covariance of a sample (
S
xy
) and of a
population (
S'
xy
):
1.
Press
CLEAR
2.
Key in the
y
-values and press
3.
Key in the
x
-values and press
. Repeat steps 2 and 3 for all data
pairs.
4.
Press
to obtain the value of
S
xy
.
5.
Press
1 1
1
to obtain
S'
xy
.
Example 1:
Find the sample covariance (
S
xy
) and population covariance
(
S'
xy
) for the following paired variables:
Keystrokes
Display
1.18
0.12
Q
(1.18)
2.1
0.02
Q
(2.1)
x
i
26
30
44
50
62
68
74
y
i
92
85
78
81
54
51
40
Keystrokes
Display
CLEAR
92
26
85
30
78
44
81
50
7.00
Total number of entries.