Calculate Weighting for Past Data
decay factor: 
  Estimate the regression constant (for binomial stats only)
regression constant: 
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x1 | x2 | |
x1 | Varx1 | Covx1,x2 |
x2 | Covx1,x2 | Varx2 |
x1 | wx2 | |
x1 | vx | rw*vt |
wx2 | rw*vt | w2vx |
x1 | wx2 | w2x3 | w3x4 | ... | wd-1xd | |
x1 | r0 | r1 | r2 | r3 | ... | rd-1 |
wx2 | r1 | r0 | r1 | r2 | ... | rd-2 |
w2x3 | r2 | r1 | r0 | r1 | ... | rd-3 |
w3x4 | r3 | r2 | r1 | r0 | ... | rd-4 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋱ | ⋮ |
wd-1xd | rd-1 | rd-2 | rd-3 | rd-4 | ... | r0 |
x1 | wx2 | w2x3 | w3x4 | ... | wd-1xd | |
x1 | w0 | w1 | w2 | w3 | ... | wd-1 |
wx2 | w1 | w2 | w3 | w4 | ... | wd |
w2x3 | w2 | w3 | w4 | w5 | ... | wd+1 |
w3x4 | w3 | w4 | w5 | w6 | ... | wd+2 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋱ | ⋮ |
wd-1xd | wd-1 | wd | wd+1 | wd+2 | ... | w2(d-1) |
x1 | wx2 | w2x3 | w3x4 | ... | wd-1xd | |
t1 | (rw)0vt | (rw)1vt | (rw)2vt | (rw)3vt | ... | (rw)d-1vt |
t0 | t1 | |
t0 | var0 | cov0,1 |
t1 | cov0,1 | var1 |
t0 | t1 | t2 | t3 | ... | tn-1 | |
t0 | var0 | cov0,1 | cov0,2 | cov0,3 | ... | cov0,n-1 |
t1 | cov0,1 | var1 | cov1,2 | cov1,3 | ... | cov1,n-1 |
t2 | cov0,2 | cov1,2 | var2 | cov2,3 | ... | cov2,n-1 |
t3 | cov0,3 | cov1,3 | cov2,3 | var3 | ... | cov3,n-1 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋱ | ⋮ |
tn-1 | cov0,n-1 | cov1,n-1 | cov2,n-1 | cov3,n-1 | ... | varn-1 |
t0 | t1 | t2 | t3 | ... | tn-1 | |
t0 | r0 | r1 | r2 | r3 | ... | rn-1 |
t1 | r1 | r0 | r1 | r2 | ... | rn-2 |
t2 | r2 | r1 | r0 | r1 | ... | rn-3 |
t3 | r3 | r2 | r1 | r0 | ... | rn-4 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋱ | ⋮ |
tn-1 | rn-1 | rn-2 | rn-3 | rn-4 | ... | r0 |
r0 |
r1
|
r2
|
r3
|
... | rn-1 | → | rn-1 |
r0 |
r1
|
r2
|
⋱ | ⋮ | ⋮ | ||
r0 |
r1
|
⋱ |
r3
|
→
|
(n-3)r3
|
||
r0 | ⋱ |
r2
|
→
|
(n-2)r2
|
|||
⋱ |
r1
|
→
|
(n-1)r1
|
||||
r0 | → |
nr0
|
h=0 | h=1 | h=2 | h=3 | |
i=0 |
r0
|
r0
|
r0
|
r0
|
i=1 | r1 |
r1
|
r1
|
r1
|
i=2 | r2 | r2 |
r2
|
r2
|
i=3 | r3 | r3 | r3 |
r3
|
If there were ever any doubts concerning the waning interest in baseball, the meeting of the magnates at Chicago during the past week must have dispelled them. The gathering was more like the meeting together of a lot of men to sing a funeral dirge than anything else. The proceedings were doleful despite the efforts of the magnates to wear smiles. Most certainly this annual meeting was far below par in enthusiasm with those of former years.
...
To be sure, those persons who court notoriety by always wanting rules changed and tinkered were at the meeting. There was no millenium plan this time; it is an exploded bladder now, but there was the new diamond notion and a few other things just as silly and just as characteristic of liquid intellects as the Utopian "plan." Of course all the venders of quack remedies pointed out that "something must be done to revive an interest in baseball." Ah! You see they admit the game's popularity is waning. Happily no changes were decided on.
BASEBALL has apparently served its day and its days seem near an end. Perhaps there may be a renaissance. But the ball players have come to the end of their string; they can play very little better; there is no more progress to be made. The people have seen it all. They are tired of reviewing it.
"I also tackled the participation rate hypothesis by replicating a variety of studies with players from Georgia, where women are strongly encouraged to play chess and the female FIDE participation rate is high at over 30%. The overall results were much the same as with the entire FIDE list, but sometimes not quite as pronounced."
"Howard debunks this by showing that in countries like Georgia, where female participation is substantially higher than average, the gender gap actually increases – which is, of course, the exact opposite of what one would expect were the participatory hypothesis true."
"I don’t know what Short is referring to here, because there is nothing in the Howard article that suggests this. Figure 1 of the study shows that the gender gap is, and has always been, lower in Georgia than in the rest of the world for the subsamples tested (top 10 and top 50). Short may be referring to Figure 2, which, to be fair, probably shouldn’t have been included in the final paper. It looks at the gender gap as the number of games increases, but on the previous page of the article, Howard himself acknowledges that accounting for number of games played supports the participation hypothesis at all levels except the very extreme."
"...This supports a nurture argument to the gender gap, but again, the sample size is too small for anything definitive to be concluded."