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