Definition of correlation coefficient
• It is used to measure how strong a relationship is between two variables. • The absolute value of the correlation coefficient gives us the relationship strength.
Understanding How the Correlation Coefficient Works
• The correlation coefficient formula is as follows –
ρxy = Cov (x, y)/σxσy
where:
ρxy =Pearson product-moment correlation coefficient
Cov (x, y) = covariance of variables x and y
σx =standard deviation of x
σy = standard deviation of y
• The correlation coefficient formulas return a value between -1 and 1, where:
a. 1 indicates a strong positive relationship.
b. -1 indicates a strong negative relationship.
c. A result of zero indicates no relationship at all.
d. Values greater than this range implies that there has been an error in the measurement.
• Correlation coefficient values less than +0.8 is not significant. If the coefficient is greater than -0.8, then that is also not considered significant.
• The most popular form of correlation coefficient is Pearson’s correlation. Pearson’s correlation is mostly used in linear regression.
• Rodgers and Nicewander have catalogued thirteen different ways of interpreting correlation. They are as follows:
a. Function of raw scores and means
b. Standardized covariance
c. Standardized slope of the regression line
d. Geometric mean of the two regression slopes
e. Square root of the ratio of two variances
f. Mean cross-product of standardized variables
g. Function of the angle between two standardized regression lines
h. Function of the angle between two variable vectors
i. Rescaled variance of the difference between standardized scores
j. Estimated from the balloon rule
k. Related to the bivariate ellipses of isoconcentration
l. Function of test statistics from designed experiments
m. Ratio of two means
Uses of Correlation coefficient
• It is most often used in finance and investing. For example, correlation can be useful in understanding how well a mutual fund performs relative to its benchmark index. • Investors can use negatively invested correlated assets to hedge their portfolios and decrease market risk due to volatility or large price fluctuations. • Correlation statistics allows investors to determine when the correlation between two variables changes. • Correlation coefficient finds its use in areas such as quantitative trading, performance evaluation and portfolio composition.
