PEARSON PRODUCT MOMENT CORRELATION COEFFICIENT
PEARSON PRODUCT MOMENT CORRELATION COEFFICIENT
Definition
It is the measure of the linear correlation between two variables X and Y
It is the measure of the strength of a linear association between two variables and is denoted by r.
It tells you how strong the linear correlation is for paired numeric data e.g. height and weight.
The Pearson correlation coefficient, r, indicates how far away all these data points are to this line of best fit.
Development
It was the imagination and idea of Sir Francis Galton that originally conceived modern notions of correlation and regression.
Developed by Karl Pearson
Purpose
The purpose of Pearson's Correlation Coefficient is to indicate a linear relationship between two measurement variables.
A. a less strong linear relationship
B. a less strong linear relationship
C. a weaker linear relationship
D. Barely there
E. a very strong non-linear relationship
F. otherwise weak relationship with an important outlier
Models
The Pearson correlation coefficient, r, can take a range of values from +1 to -1.
A value of 0 indicates that there is no association between the two variables.
A value greater than 0 indicates a positive association; that is, as the value of one variable increases, so does the value of the other variable. A value less than 0 indicates a negative association; that is, as the value of one variable increases, the value of the other variable decreases.
Models
SAMPLE PROBLEM:
With the data below, test if age and income are related:
Subject
Age
Monthly Income (in 1,000)
1
18
15
2
25
29
3
57
68
4
45
52
5
26
32
6
64
80
7
37
41
8
40
45
9
24
26
10
33
33
1. State the hypothesis:
Ho : There is no significant relationship between age and income.
Ha: There is a significant relationship between age and income.
2. Set the level of significance
Alpha (α) = 0.05
Calculate the degrees of freedom: df = n-2 = 10-2 = 8
Critical value in the r table:
Critical r α .05 is 0 .6319
If computed r > 0.6319, reject the
Definition
It is the measure of the linear correlation between two variables X and Y
It is the measure of the strength of a linear association between two variables and is denoted by r.
It tells you how strong the linear correlation is for paired numeric data e.g. height and weight.
The Pearson correlation coefficient, r, indicates how far away all these data points are to this line of best fit.
Development
It was the imagination and idea of Sir Francis Galton that originally conceived modern notions of correlation and regression.
Developed by Karl Pearson
Purpose
The purpose of Pearson's Correlation Coefficient is to indicate a linear relationship between two measurement variables.
A. a less strong linear relationship
B. a less strong linear relationship
C. a weaker linear relationship
D. Barely there
E. a very strong non-linear relationship
F. otherwise weak relationship with an important outlier
Models
The Pearson correlation coefficient, r, can take a range of values from +1 to -1.
A value of 0 indicates that there is no association between the two variables.
A value greater than 0 indicates a positive association; that is, as the value of one variable increases, so does the value of the other variable. A value less than 0 indicates a negative association; that is, as the value of one variable increases, the value of the other variable decreases.
Models
SAMPLE PROBLEM:
With the data below, test if age and income are related:
Subject
Age
Monthly Income (in 1,000)
1
18
15
2
25
29
3
57
68
4
45
52
5
26
32
6
64
80
7
37
41
8
40
45
9
24
26
10
33
33
1. State the hypothesis:
Ho : There is no significant relationship between age and income.
Ha: There is a significant relationship between age and income.
2. Set the level of significance
Alpha (α) = 0.05
Calculate the degrees of freedom: df = n-2 = 10-2 = 8
Critical value in the r table:
Critical r α .05 is 0 .6319
If computed r > 0.6319, reject the