Define: Coefficient Of Correlation R

The coefficient of correlation (R) is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation.

The coefficient of correlation (R) is calculated by dividing the covariance of the two variables by the product of their standard deviations. The formula for calculating R is: R = Cov(X, Y) / (SD(X) * SD(Y)), where Cov represents covariance and SD represents standard deviation.

A positive coefficient of correlation (R) indicates a direct or positive relationship between the two variables. This means that as one variable increases, the other variable also tends to increase.

A negative coefficient of correlation (R) indicates an inverse or negative relationship between the two variables. This means that as one variable increases, the other variable tends to decrease.

No, the coefficient of correlation (R) cannot be greater than +1 or less than -1. It is bound by these limits and represents the maximum strength of the linear relationship between the variables.

The coefficient of correlation (R) can be interpreted as a measure of the proportion of variability in one variable that can be explained by the other variable. For example, an R value of 0.8 indicates that 64% (0.8^2) of the variability in one variable can be explained by the other variable.

No, the coefficient of correlation (R) only measures the strength and direction of the linear relationship between variables. It does not provide evidence of causation. Establishing causation requires additional research and analysis.

Yes, the coefficient of correlation (R) can be used to compare relationships between different sets of variables. It allows for the comparison of the strength and direction of the linear relationships, regardless of the units or scales of the variables.

Yes, the coefficient of correlation (R) can be used to predict future values to some extent. By knowing the relationship between two variables, one can make reasonable predictions about the value of one variable based on the value of the other variable. However, it is important to note that correlation does not imply causation, and other factors should also be considered for accurate predictions.