By examining the scatter plot, we see that these two variables are positively correlated: We already know that these are two different quantities with different measurement units, i.e. Here is a quick summary: summary(cars) # speed dist There are 50 observations and 2 variables in this dataset that are the speed and stopping distances of cars. I am going to use the cars data from the R library. I would like to share my insights with you. I tried to clarify this in my mind by applying these concepts on a dataset. And yes, sometimes r 2 and R 2 are the same thing, but sometimes they are not. There are actually 3 different concepts here: 1.correlation coefficient ( r) 2.squared correlation coefficient ( r 2) and 3. R 2 on the other hand, cares about the distances between points, and it can go to negative values pretty quickly (although most people believe that it ranges between 0 and 1 since it is a ratio and squared value!), if two signals have different means. it isn’t affected by the differences in the means. r doesn’t care about the signal amplitudes, i.e. r generates a value between -1 and 1, and reflects if two signals covary, meaning if they increase or decrease together. My motivation in using r and R-square, of course, was to evaluate the similarity between actual and predicted EMG signals. I searched this online and saw that almost everbody was saying the same thing: coefficent of determination is simply the squared correlation coefficient (r 2)! They told me that there was no need to report both r and R 2, because R 2 was simply the square of the r. Unfortunately, I received some criticism from a committee member during my defense and also from a reviewer when I submitted my paper. I built a linear model and I reported my prediction accuracy in two forms: the correlation coefficient (r) and the coefficient of determination (R-squared or R 2). In graduate school, I worked on a project in which I used neural signals to predict the forelimb EMG signals in rats. Squared correlation and R-squared: When they are (NOT) the same thing?
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