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Things may be correlated without causal relationship or conversely.
Consider the Modulus function - that is the value of a number without regard to its sign. Over any domain (-a,a), there is a very strict relationship between x and mod(x), but their correlation is 0.
Conversely, I expect that there is a good correlation between my age and the number of TV sets in the world. That is not to say that my getting older is producing more TVs or that TV production is causing me to age. Simply that both of them are correlated to a third variable - time. There can be correlation without such a third variable but, offhand, I cannot think of an example.
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What does a relationship between two correlated variables have?
Correlation between two variables implies a linear relationship between them. The existence of correlation implies no causal relationship: the two could be causally related to a third variable. For example, my age is correlated with the number of TV sets in the UK but obviously there is no causal link between them - they are both linked to time.
What value or benefit would a researcher gain by calculating a correlation coeffcient rather than simply describing the relationship as a positive correlation or a negative correlation?
The correlation coefficient gives a measure of the degree to which changes in the variables are related. However, the relationship need not be causal.
What is implied when it is said that x and y have a negative correlation?
It is implied that x increases when y decreases and conversely. There is no implication about a causal relationship.
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?
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.
What is the meaning of positive correlation?
Two variables are said to be positively correlated if an increase in one is accompanied by an increase in the other. There need not be any causal link between these changes.
