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NFL Sunday critical field goals  OT (math)
Posted By: Casper van der Tak
Date: Wednesday, 25 January 2012, at 3:43 p.m.
In Response To: NFL Sunday critical field goals  OT (math) (Chuck Bower)
I am still not sure what you did. A few remarks:
Did you try to estimate a log form? Log (r) = p + q * log (distance)? That way you can test for the appropriate form (linear, cubic, quadratic, or any other power). (This is probably the remark that can be used with the least effort and the most possible return on time spent)
Did you take into account the number of observations in your weighting (not sure about how you weighted)?
Technically, you cannot use least squares because your success rate is between 0 and 1. You are supposed to use an estimator like Probit (sorry, no more info, long time ago that I did any econometrics). This may well be a bit of nit picking BTW, it depends on your data.
I am not sure, but maybe you need to look into error in variable models. Normal regressions assume that distance is measured exactly, not sure that that would apply here. This is complicated, so if you believe distances as reported are reasonably accurate (say plus minus 1 yard), better forget about it.

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