Pearson’s Linear Correlation Coefficient  Given: At a concert, the number of tattoos, x, and the number of piercings, y, that a.

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Transcript Pearson’s Linear Correlation Coefficient  Given: At a concert, the number of tattoos, x, and the number of piercings, y, that a.

Slide 1

Pearson’s Linear Correlation Coefficient
 Given: At a concert, the number of tattoos, x,
and the number of piercings, y, that a person had
was recorded:
x

y

2
8
5
3
6

5
7
6
4
8

 Find: The linear correlation coefficient, r
1

The Formula
 The value of Pearson’s linear correlation coefficient, r, is found
using formula 3.2:
SS(xy)
r=
 SS(x) • SS(y)
Note: The formula for r uses the 3 SS values found as preliminary
calculations
If you do not know the values of SS(xy), SS(x) and SS(y), you
need to obtain them before continuing
(See Animated Tutorial “Bivariate Data - Preliminary Calculations”
for assistance in completing these preliminary calculations)

 Once you have the values of SS(xy), SS(x) and SS(y), you are
prepared to proceed with the calculations of r
2

Calculating r
 The preliminary calculations yielded:

SS(x) = 22.8
r=

=

SS(xy)
 SS(x) • SS(y)
12
 228

=

SS(y) = 10
=

SS(xy) = 12

12
 (22.8) • (10)

12

= 0.7947

r = 0.79

15.099669

Notes: 1) Do not use rounded values for the SS values
2) Round only when the calculation is completed
3) Typically, r is rounded to the nearest hundredth
3


Slide 2

Pearson’s Linear Correlation Coefficient
 Given: At a concert, the number of tattoos, x,
and the number of piercings, y, that a person had
was recorded:
x

y

2
8
5
3
6

5
7
6
4
8

 Find: The linear correlation coefficient, r
1

The Formula
 The value of Pearson’s linear correlation coefficient, r, is found
using formula 3.2:
SS(xy)
r=
 SS(x) • SS(y)
Note: The formula for r uses the 3 SS values found as preliminary
calculations
If you do not know the values of SS(xy), SS(x) and SS(y), you
need to obtain them before continuing
(See Animated Tutorial “Bivariate Data - Preliminary Calculations”
for assistance in completing these preliminary calculations)

 Once you have the values of SS(xy), SS(x) and SS(y), you are
prepared to proceed with the calculations of r
2

Calculating r
 The preliminary calculations yielded:

SS(x) = 22.8
r=

=

SS(xy)
 SS(x) • SS(y)
12
 228

=

SS(y) = 10
=

SS(xy) = 12

12
 (22.8) • (10)

12

= 0.7947

r = 0.79

15.099669

Notes: 1) Do not use rounded values for the SS values
2) Round only when the calculation is completed
3) Typically, r is rounded to the nearest hundredth
3


Slide 3

Pearson’s Linear Correlation Coefficient
 Given: At a concert, the number of tattoos, x,
and the number of piercings, y, that a person had
was recorded:
x

y

2
8
5
3
6

5
7
6
4
8

 Find: The linear correlation coefficient, r
1

The Formula
 The value of Pearson’s linear correlation coefficient, r, is found
using formula 3.2:
SS(xy)
r=
 SS(x) • SS(y)
Note: The formula for r uses the 3 SS values found as preliminary
calculations
If you do not know the values of SS(xy), SS(x) and SS(y), you
need to obtain them before continuing
(See Animated Tutorial “Bivariate Data - Preliminary Calculations”
for assistance in completing these preliminary calculations)

 Once you have the values of SS(xy), SS(x) and SS(y), you are
prepared to proceed with the calculations of r
2

Calculating r
 The preliminary calculations yielded:

SS(x) = 22.8
r=

=

SS(xy)
 SS(x) • SS(y)
12
 228

=

SS(y) = 10
=

SS(xy) = 12

12
 (22.8) • (10)

12

= 0.7947

r = 0.79

15.099669

Notes: 1) Do not use rounded values for the SS values
2) Round only when the calculation is completed
3) Typically, r is rounded to the nearest hundredth
3