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The relationship between two random independently distributed variables is considered to be theoretically the weakest when the correlation coefficient is zero and theoretically the strongest when the correlation coefficient is one, indicating a positive relationship between two variables and negative one, indicating a negative relationationship between two variables.
I state that this is a theoretical result as if variables are not random, independently distributed, then a high correlation coefficient can result. For example, let us say that we obtained the following data on age and frequency of accidents:
Age 18 1 in 18 people have accidents in a year
Age 25 1 in 25 people have accident in a year
Age 30 1 in 30 people have accidents in a year
Age 35 1 in 6 people have accidents.
Age 40 1 in 400 people have accidents
If I selectively calculated a correlation coefficient this data including only the three groups ages 18, 25 and 30, you can see I will have a correlation coefficient of 1, however the data was not a random sample of all ages.
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When there is no linear correlation the correlation coefficient equals?
0
What is the strongest a correlation could be?
Either +1 (strongest possible positive correlation between the variables) or -1 (strongest possible negativecorrelation between the variables).
What is the range of correlation coefficient and what does its value tell?
The product-moment correlation coefficient or PMCC should have a value between -1 and 1. A positive value shows a positive linear correlation, and a negative value shows a negative linear correlation. At zero, there is no linear correlation, and the correlation becomes stronger as the value moves further from 0.
Correlation coefficient value mean?
The correlation coefficient is a measure of linear association between two (or more) variables. It does not measure non-linear relationships nor does it say anything about causality.
When doing linear regression if the correlation coefficient is positive the slope of the line is negative?
False.
