is coefficient of correlation and coefficient of determination the same thing? or different?
Different, r versus r^2.
thnx
The coefficient of correlation and the coefficient of determination are related but not the same thing. Let me explain.
The coefficient of correlation, commonly denoted as "r," measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1. A positive value indicates a positive correlation, meaning that as one variable increases, the other tends to increase as well. A negative value indicates a negative correlation, where as one variable increases, the other tends to decrease. Zero indicates no correlation between the variables.
To calculate the coefficient of correlation, you would typically use a statistical software or a calculator specifically designed for this purpose. However, here is a general outline of the steps involved:
1. Gather a dataset with paired observations for the two variables of interest.
2. Calculate the mean (average) of each variable.
3. For each pair of observations, find the deviation of each variable from its mean.
4. Multiply the deviations of both variables for each pair, and sum those products.
5. Divide the sum of the products by the product of the square root of the sum of squared deviations for each variable.
6. The resulting value is the coefficient of correlation (r).
On the other hand, the coefficient of determination, often represented as "r-squared," is a measure that explains the proportion of the variance in the dependent variable that can be predicted from the independent variable(s). It is the square of the coefficient of correlation (r) and ranges from 0 to 1. An r-squared value of 0 indicates that the independent variable(s) cannot explain any of the variation in the dependent variable, while a value of 1 means that all the variation can be explained.
To calculate the coefficient of determination, you can simply square the coefficient of correlation (r). Thus, if you already know the coefficient of correlation, finding the coefficient of determination is a straightforward computation.
In summary, while the coefficient of correlation measures the strength and direction of the linear relationship between variables, the coefficient of determination represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s).