@mdinnerspaceOne last time before I give up.
In post #62, you proposed two formulas:
A: FIDE = -78 + 1 * Blitz + 0 * Classical
B: FIDE = -169 + 0 * Blitz + 1 * Classical
In post #76,
@Sarg0n proposed a third formula:
C: FIDE = -123.5 + 0.5 x Blitz + 0.5 * Classical
In post #1, I proposed a fourth formula:
D: FIDE = 187 + 0.48 * Blitz + 0.38 * Classical
Using any of these formulas, we can calculate the squared prediction error like this:
Predicted FIDE = 187 + 0.48 * Blitz + 0.38 * Classical
Squared error = (Actual FIDE - Predicted FIDE)^2
The first observation (user profile) in my dataset looks like this:
* Username: 2Ap
* FIDE rating: 2078
* Blitz rating: 2217
* Classical rating: 2239
For this specific user, the squared prediction error with each formula is:
A : (2078 - (-78 + 1 * 2217 + 0 * 2239))^2 = 3721
B: (2078 - (-169 + 0 * 2217 + 1 * 2239))^2 = 64
C: (2078 - (-123.5 + 0.5 * 2217 + 0.5 * 2239))^2 = 702.25
D: (2078 - (187 + 0.38 * 2217 + 0.48 * 2239))^2 = 685.39
In that example, it looks like your formula B is the most accurate (followed by mine), since it produces the smallest squared prediction error. So the question becomes: Is your formula B most accurate overall, or was the case of player 2Ap a fluke?
To answer this, we calculate the squared prediction error for each of the 2807 players in the sample. Then, we take the sum of those squared errors to see which formula is more precise OVERALL.
The sum of squared errors per formula are as follows:
A: 400100865
B: 405032490
C: 387459623
D: 366554861
Out of the four proposed formulas, your two formulas are the worst at predicting FIDE ratings. The best one is the one I proposed in the original post. In fact, it is mathematically impossible to find different weights that produce smaller total squared errors than mine. That’s a feature of the least squares regression estimator that I used.
And to answer your question directly, I didn’t pull the 187 number out of nowhere. 187 is the estimated intercept of the linear regression model. This was explicit in the original post, and the intercept is a well-known concept which I teach to all my first-year intro to stats students.
Your calculations aren't a "proof" of anything, except your lack of understanding.