Thursday, September 17, 2009

Parks Half-Marathon Formalized

So far I’ve used this blog to describe economics issues of interest to my professional experience. This blog will continue to chronicle those events as my skills are often of most use there. On occasion, some personal event will provide an opportunity to utilize the lessons of economics in a practical way.

Last weekend, I participated in a half-marathon (a 13.1 mile run for the uninitiated). Sure it tested my health but it’s after effect provided a great statistical inquiry. Analysis of the Parks provides a few lessons.

I. Age is of little matter to runners. My results show that age, while statistically significant, has little impact on the timing of a run. In fact, I show below that increasing age by one year increases the total finish time by less than one minute. That’s very impressive when you consider that this equates to an addition of less than 5 seconds per mile.

a. This is course panel data rather than time-series data. While there is little difference amongst people of different ages in this sample it is unclear that runners in this sample will maintain this pattern as they themselves age.

II. Gender does matter. Men run almost 15 minutes faster than their female counterparts of equal age.

Now that you’ve got the headline lets delve into the proof.

Figure 1 below shows the distribution of finish times, in minutes, of all runners at the September 2009 Parks half.

We can see that the values bunch around 120 minutes. Ten percent of runners finish in 98 minutes or less and fifty percent of runners finish in 122 minutes or less.

While this is a helpful way to look at the data, it provides little explanation as to why it occurs. The only other information available about runners is their age, gender, and city/state of residence. I have taken the age and gender of runners to explain finish times.

The results of a linear regression of the finish time based on these variables are in Table 1 below.

Table 1 shows that both variables are statically significant. I’ve used the age difference from (current age-38), as 38 is the median sample age (this should not impact the size of the coefficient but it makes it easier to understand our baseline who is a 38 year old female). The table shows that men finish about 15 minutes earlier than women of similar age and that aging by one year adds about 40 total seconds to finish time.

According to my model, I should have finished my race in about 10 less minutes than I did. This is encouraging. I means that I should be able to PR with some ease in my next outing and that with age I won’t gain too much time.

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