This calculation can be summarized in the following equation: ρxy=Cov(x,y)σxσywhere:ρxy=Pearson product-moment correlation coefficientCov(x,y)=covariance of variables x and yσx=standard deviation of xσy=standard deviation of y\begin{aligned} &\rho_{xy} = \frac { \text{Cov} ( x, y ) }{ \sigma_x \sigma_y } \\ &\textbf{where:} \\ &\rho_{xy} = \text{Pearson product-moment correlation coefficient} \\ &\text{Cov} ( x, y ) = \text{covariance of variables } x \text{ and } y \\ &\sigma_x = \text{standard deviation of } x \\ &\sigma_y = \text{standard deviation of } y \\ \end{aligned}ρxy=σxσyCov(x,y)where:ρxy=Pearson product-moment correlation coefficientCov(x,y)=covariance of variables x and yσx=standard deviation of xσy=standard deviation of y. The value of coefficient of correlation is always 2. B. Instead, the poorly-performing bank is likely dealing with an internal, fundamental issue. The formula was developed by British statistician Karl Pearson in the 1890s, which is why the value is called the Pearson correlation coefficient (r). A correlation coefficient is a value between -1 and 1 that shows how close of a good fit the regression line is. A value of -1.0 means there is a perfect negative relationship between the two variables. The value of a correlation coefficient lies between -1 to 1, -1 being perfectly negatively correlated and 1 being perfectly positively correlated. This means that as x increases that y also increases. Therefore, correlations are typically written with two key numbers: r = and p =. By dividing covariance by the product of the two standard deviations, one can calculate the normalized version of the statistic. The coefficient of correlation always lies between –1 and 1, including both the limiting values i.e. Correlation Coefficient The correlation coefficient, r, is a summary measure that describes the extent of the statistical relationship between two interval or ratio level variables. R square is simply square of R i.e. The correlation coefficient is calculated by first determining the covariance of the variables and then dividing that quantity by the product of those variables’ standard deviations. The larger the absolute value of the coefficient, the stronger the relationship: The extreme values of -1 and 1 indicate a perfect linear relationship when all the data points fall on a line. If there is a complete and strong correlation between two variables, the values are either +1 or -1, depending on whether it is a positive or a negative correlation. Correlation is one of the most common statistics. -1 to 1 Correlation coefficient is the measure of linear strength between two variables, and it can only take value form -1 to 1 Negative values implying a negative (downward) relationship, while positive values imply a positive (downhill) relationship. The well known correlation coefficient is often misused because its linearity assumption is not tested. For example, a correlation can be helpful in determining how well a mutual fund performs relative to its benchmark index, or another fund or asset class. 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