This is almost certainly an extremely novice question, but it is one that I am struggling to wrap my head around.
I am enrolled in a Master's Statistics course, and we just recently covered correlation and regression. While I would say that I understand the concepts relatively well, I am a bit confused on some nuances between the two.
I am speaking of simple linear regression --- only two variables.
I know that regression allows for prediction of y in terms of x, which is something that standard Pearson's correlations cannot do. I also know that in order to gauge whether the regression model is robust in terms of the explained relationship, one might wish to calculate the Coefficient of Determination (which is r^2, or SSR/SST). I am struggling to see the connection between this.
I recognize that the Pearson's correlation coefficient is a component of the regression slope, but it is not the only component. As such, the regression coefficient and Pearson's correlation coefficient are different. So, then, why is the coefficient of determination for regression calculated using the Pearson's correlation coefficient, and not the regression coefficient?
Looking for big picture/analytical responses in a way that is tailored to my skill level --- don't need to derive proofs! I just need to bridge this connection in my mind, as it is unclear.
Thanks!