00:01
All right.
00:02
So we're looking at spurious correlations, which is something that refers to the apparent relationship between variables, but they have no true relationship or not related to other variables.
00:15
So the correlation we're looking at is the championship, the major sports championship and the performance of a stock index in that year.
00:24
And the indicator states that when a team from a particular conference wins the championship, the stock index will increase.
00:30
So in other words, wins corresponds with an increase in stock index, some stock index.
00:43
But we know that those things are probably not really correlated, not related, but there's no relationship between them, but there's some correlation there.
00:54
And that's a spurious correlation.
00:59
We're going to assume that this indicator has, so assuming the indicator, the indicator, has no predictive value, that means our probability would be a half.
01:21
And we're going to look at, and since this first championship was held, the indicator has been correct 48 out of 57 times, which is a probability of 0 .84, which is crazy.
01:31
Like, wow, that's a pretty strong indicator.
01:34
So let's see what's, if there's no predictive value, though, we'd say the probability is a half.
01:39
So how do we interpret this? so this is a binomial experiment.
01:44
So probability of x equals n choose x.
01:47
P to the x times 1 minus p to the n minus x in this case n is 57 so we do 57 choose x p is a half so 1 minus a half is a half so it's 57 minus x and since these have the same base we can add the exponents so the x minus x great, this is our distribution.
02:25
So what we do is we want to find the probability of 48 or more times.
02:31
What's the probability that the indicator would be correct, 48 or more times in 57 years? so that means we basically take the sum of all the x equals 48, add to it the probability of x equals 49, and so on and so forth, all the way down to the probability x equals 57.
02:54
So we take our function, substitute x is 48, 49, 50, and so and so forth, all the way to 57, and we add up these probabilities.
03:03
And we get this, something very close to zero.
03:06
So this would say, wow, that's a very rare occurrence of 48 out of 57.
03:10
So that means there's something going on there.
03:12
But that's a spurious correlation because these things probably have no true relation between the stock index and the wins of a championship.
03:23
And then for part b, we're doing the same thing...