Coefficient of determination. I think the point you are going for is coefficient of correlation (which you square to get R^2). Correlation does not fit a line. Correlation only tells you how well two variables relate to one another. They are related, but not the same.
For a predictive model to be a bit efficient any variables that are chosen as an explanatory variable better have high correlation with the depending variable otherwise predictions generated from any model is going to be ineffective.
R^2 presents a stat that actually tells you what percentage of your model is explained by the independent variable. Most of the folks that put up stats on their websites do not post any r^2. Would you trust the results of the model that has low r^2?
Your parameters in any regression model in simple terms is nothing but a slope. Th convergence to mean theory only works if model is very well specified.
As an example, in your previous post (not this one) you had mentioned analytics use probabilities to derive the “expected value” (I.e. mean)
However in Hockey the expected outcomes should be modeled using conditional probabilities not simple models that many stats blowhards use
Example(simple)
HDCF%: the model is not allowed to be adjusted for high danger areas where the shooter was actually well defended or left wide open or did the shooter bobble the puck or etc......
There is no dataset that currently exists to allow for such analysis; the results can be heavily biased.
Another example: PDO = SV% + SH%
Both Sh% and Sv% both these metrics are a mathematical fiction of of two variables
Sv% (team defense, opposition offense, goalie)
Sh%(team offense, opposition defense, opposition goalie)
There are no metrics available to quantify which one of these are driving either the sh% or sv% yet people are quick to use PDO as a bottom line without understanding the limitation of the stat and the kind of bias it already has.
I could go on and on and on but there are people who
1. get the math and stat and limitations associated with it,
2. there are people that are completely blind to the limitation because their knowledge of stats is weak (or their ego is massive to accept the limitations-what I say is right screw everyone else)
3. and there are people who completely ignore the stats.
Some fall in the first category (I’m there), majority of the posters who use stats here fall in the second category and the remainder in the third category. It’s a shame that vocal community belongs in the second category (look at mirtle; he is a journalist but using stats like they are TRUTH; if he was a statistician he would exercise caution and if he was a mathematician he would throw the probabilities out of the window)