Question

 The Correlation Coefficient

05 Aug 2026
Answer :
Word Count : 512
The correlation coefficient is a statistical measure used to determine the degree and direction of relationship between two quantitative variables. In quantitative analysis for managerial applications, it is widely used to understand how changes in one variable are associated with changes in another. For example, a manager may study the relationship between advertising expenditure and sales, income and consumption, price and demand, or employee training and productivity. The most commonly used measure is Pearson’s correlation coefficient, denoted by (r). Its value always lies between (-1) and (+1). The formula is: [ r=\frac{N\sum XY-(\sum X)(\sum Y)} {\sqrt{[N\sum X^2-(\sum X)^2][N\sum Y^2-(\sum Y)^2]}} ] where (X) and (Y) represent the two variables and (N) represents the number of observations. The value of the correlation coefficient indicates both the strength and direction of the relationship. When (r=+1), there is a perfect positive correlation, meaning that an increase in one variable is associated with a proportional increase in the other. When (r=-1), there is a perfect negative correlation, meaning that an increase in one variable is associated with a
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