In statistics correlation refers to relationship between
two variables. When the value of one variable varies closely with variation in another,
the two variables are said to be correlated. For example if the sale of umbrellas in a
town during the rainy season is found to vary with the the amount of rainfall during the
season than we can say that the sale of umbrella and amount of rainfall are
correlated.
Correlation coefficient is a statistical
measure of how close this relationship is. A correlation coefficient of 1 indicates a
perfect or total dependence between two variables. For example, if we were to calculate
the correlation coefficient between temperature in Fahrenheit and Celsius it will be
equal to 1. A correlation coefficient of -1 means the variables are inversely
correlated. For example, the volume of a given weight of different substances is
inversely proportional to their densities therefore the correlation coefficient between
these two will be -1. A correlation coefficient of 0, implies no correlation. But in
reality this only implies that there is no linear relationships. For example some graphs
of two related variable have shapes lie 'U' or 'inverted U'. In these cases the
relationship exists but is not linear. Therefore correlation coefficient is likely to be
close to 0.
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