I am trying to clarify the concept of Pearson's correlation coefficient, r. I am aware that correlation coefficient is a measure of the strength of a linear association. But, is it correct to say the following?
Correlation coefficient describes how closely the data points cluster around a line (of best fit)
My lecture notes state that "In general, the closer the points are to a straight line formed, the stronger the correlation between the two variable". However, we also know that scale of the data set does not affect correlation coefficient. In other words, I can increase the scale, thereby increasing the distance of the data points to the line of best fit, yet the correlation coefficient does not change. This contradicts what is stated in my notes.
I will appreciate any help with clarifying this concept.