Practical Statistical Modeling: The Dreaded After-School Carpool Pickup

The Little Man started kindergarten this week. It meant a new school, and the new school has one of these well-organized systems of picking up your kids at the end of the day. But it can be a bit intimidating the first time. Basically, it works like this:

You arrive at the school and pull around to a side parking area. Four lanes are set up. Each lane holds about 10 cars, and the lanes are filled in order, first lane first, then the second, and so on. When all lanes are filled, the area is closed. Cars that don’t make the first round, line up in the upper parking areas for the second round. The students are released, the go to their cars. When all students are in the cars, the lanes are released in order. This is then repeated for the second round.

It’s very organized and efficient, but there if you want to be in that first round, or that first lane, you have to get there pretty early. As someone who doesn’t really want to sit in the car for half an hour, I decided I’d get there early on the first two days to capture data about when cars arrive, and build a statistical model based on that. Which is exactly what I did. I arrived early, getting into the first half of the first lane, and then noted the arrival times, and lane positions of the other cars in the first round. I did this for two days, and then built my model.

Constructing the model

The  model was fairly simple. I used a negative number to represent the number of minutes before dismissal (a kind of t-minus 10 minutes) that a car arrived. With that number, I gave the number of the car. So at t-21 minutes, car 16 and 17 arrived. Since each lanes holds 10 cars, it’s pretty easy to determine which lane (and which slot in a lane) the car is in. I ran a correlation on my data and got a very strong correlation: 0.951. The r-squared came to 0.905. I then plotted the data in a scatterplot, and annotated it to better illustrate the lanes. Here is what the results look like:

Carpool Model
Click to enlarge

As you can see, the data makes it clear that in order to make the first round, I’d need to arrive no later than 7 minutes before dismissal. If I want to be in the first lane, I need to arrive no later than 24 minutes before dismissal.

Adding practicality

Of course, it would be a little more practical if the model told me when to leave the house. I hadn’t thought to note the time I left the house and arrived at the school each day, but it didn’t matter. I grabbed the data from my Automatic Link device, and was able to determine that it took, on average, 6 minutes to drive from the house to the school. To be safe, I added 1 minute to this number, and then came up with the following table:

Departure Times

So now, I know that if I want to be in that first round of pickups, I need to leave the house no later than 14 minutes before the students are dismissed. That information could end up saving quite a bit of time over the course of the year. I tend to like to get places early, but I have to balance that against other things I need to get done. Knowing that I don’t have to leave the house half an hour early buys me an extra 15 minutes/day. That doesn’t sound like much, but, I can write a page and a half in 15 minutes. So it’s something.

5 thoughts on “Practical Statistical Modeling: The Dreaded After-School Carpool Pickup

  1. If I had similar skills, I’d do the same thing. I love reading your blog. Keep up the good work.

  2. Be prepared to have the entire schedule thrown off if there is rain. On average, I have to leave 8-10 minutes earlier than the normal time to get the same spot on a bad weather day.

  3. and now we all know why the other kids put “kick me” signs on your back during elementary school… and other parents do it now at the PTA meeting 😉

    j/k – that is awesome work, man!

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