What is correlation What are the different types of correlation Why is it important to determine correlation What does it mean when it is said that two variables have no correlation?

Answer 1

A correlation is the relationship between two or more variables.

Correlations are described as either weak or strong, and positive or negative. There can be a perfect correlation between variables, or no correlation between variables.

It is important to determine the correlation between variables in order to know if and how closely changes in one variable are reflected by changes in another variable. This is done by determining the coefficient of correlation (r), which describes the strength of the relationship between variables and the direction.

-1 ≤ r ≤ +1

if r= +1 or -1, there is a perfect correlation

if r= 0 there is no correlation between the variables.

a value closer to + or - 1 demonstrates a strong correlation, while a value closer to 0 demonstrates a weak correlation.

a + value demonstrates that when one variable increases the other variable increases, while a - value demonstrates that when one variable increases the other variable decreases.

However, it is very important to understand that correlation is not the same as relationship. Consider the two variables, x and y such that y = x2 where x lies between -a and +a. There is a clear and well-defined relationship between x and y, but the correlation coefficient r is 0. This is true of any pair of variables whose graph is symmetric about one axis.

Conversely, a high correlation coefficient does not mean a strong relationship - at least, not a strong causal relationship. There is pretty strong correlation between my age and [the log of] the number of television sets in the world. That is not because TV makes me grow old nor that my ageing produces TVs. The reason is that both variables are related to the passage of time.