# Correlation

• Charan Singh Rayat
Chapter

## Abstract

So far, we have learned to compute certain mathematical measures, representing the performance or behavior of a set of observations. Instead of studying the performance of two sets separately, it would be of great importance to examine the relationship of one set of observations with the other one. Two variables are said to be “correlated” if an increase or decrease in one variable is associated with an increase or decrease in the other. If higher values of one variable are associated with higher values of the other or when the lower values of one variable are associated with the lower values of the other, then it is said to be “directly correlated” or “positively correlated.”

In other words, with an increase/decrease in one variable, the other also increases/decreases, respectively. This is said to be positive or direct correlation. On the other hand, in “negative correlation or inverse correlation” with an increase in one variable, the other variable decreases, or with a decrease in one variable, the other variable increases. Pearson’s coefficient of correlation is a measure of the degree of relationship between the two variables. It is denoted by “r” in the case of sample estimate and by “ρ” in the case of the correlation obtained from the whole population. The applications of various formulae for computing “coefficient of correlation” would be dispensed with solved examples in this chapter.