This is an excellent topic, and this is a good start, but I think this post could use some work. In fact, if you wanted focused help with this, I would be interested in writing this with you. You can email me at jsalvatier@gmail.com or talk to me on skype (jsalvatier).
The way you’ve described this is a little vague, I think, and also makes the concept seem more complex than it is. I also think it would be useful to explore ways in which regression to the mean can lead you astray.
The core of regression to the mean is not that complicated: take a set of variables for which it’s semi realistic to say they’re independently and identically distributed (that is they have the same distribution and each one is a separate realization from that distribution). For example, the number of pushups you can do each day this week, or the number of minutes you’re early/late for school each day. If you notice that a value is unusually high compared to ones that came before it, then later values are likely to be lower than it. If one value is higher than the mean of the distribution, then ,on average, later values will be below it because the mean of these variables is the mean of the distribution.
Here’s an illustration which I think might help: Lets say you’re a math teacher and you have the students take two tests during the year. After a while, you notice that students who did really well on the first test tend to do worse than before on the next test. It may be tempting to conclude that this is because students are afraid of success, or worried about doing too much better than their peers or because students get lazy when they’re successful. However, there’s a simpler explanation, tests are noisy measurements, so students who did very well on the first test are probably good students but also got a bit lucky. If they had been unlucky, they might have still been quite good, but not at the top. Since on the next test each person is just as likely to be lucky as unlucky (the mean of luck is 0), they’ll probably do worse the next time around.
You also mention stock returns. I think it would be good to explain why “go invest all your money in the mutual fund that did the best last year” isn’t a very effective strategy.
This is an excellent topic, and this is a good start, but I think this post could use some work. In fact, if you wanted focused help with this, I would be interested in writing this with you. You can email me at jsalvatier@gmail.com or talk to me on skype (jsalvatier).
The way you’ve described this is a little vague, I think, and also makes the concept seem more complex than it is. I also think it would be useful to explore ways in which regression to the mean can lead you astray.
The core of regression to the mean is not that complicated: take a set of variables for which it’s semi realistic to say they’re independently and identically distributed (that is they have the same distribution and each one is a separate realization from that distribution). For example, the number of pushups you can do each day this week, or the number of minutes you’re early/late for school each day. If you notice that a value is unusually high compared to ones that came before it, then later values are likely to be lower than it. If one value is higher than the mean of the distribution, then ,on average, later values will be below it because the mean of these variables is the mean of the distribution.
Here’s an illustration which I think might help: Lets say you’re a math teacher and you have the students take two tests during the year. After a while, you notice that students who did really well on the first test tend to do worse than before on the next test. It may be tempting to conclude that this is because students are afraid of success, or worried about doing too much better than their peers or because students get lazy when they’re successful. However, there’s a simpler explanation, tests are noisy measurements, so students who did very well on the first test are probably good students but also got a bit lucky. If they had been unlucky, they might have still been quite good, but not at the top. Since on the next test each person is just as likely to be lucky as unlucky (the mean of luck is 0), they’ll probably do worse the next time around.
You also mention stock returns. I think it would be good to explain why “go invest all your money in the mutual fund that did the best last year” isn’t a very effective strategy.