UtilityMinimization

Professor Charles Stanton of California State University, San Bernardino has put up a nifty tool that can help in the understanding of linear regression. The java applet allows you to place regression points on a Cartesian plane. Once you put down two points, the applet draws a regression line and gives you the equation for the line. As you add more and more points, the line and the equation update in real time. It’s fun to see how outliers can completely give false results. Check it out here.

The US Department of Education recently released a report comparing public and private schools. The study used the National Assessment of Educational Progress (NAEP) data, which is a nationally representative sample of public and private school students. This particular study looked at reading and math test performance of students in the fourth and eighth grades. Part of the results of this study were covered in today’s New York Times, which reported that fourth grade students in public schools do significantly better than fourth graders in charter schools. This result calls into question the agenda of charter schools, which, as a centerpiece of the Bush education plan, claim to be able to produce better results at a lower cost.

While the results regarding charter schools are interesting, I do want to point out a few things. First of all, the report is really about comparing all private students to public school students. The results from this overall study were equally interesting. For fourth grade reading scores, the average private school student did better in reading. After controlling for differences in student characteristics, however, the difference in reading scores was not different than zero. For fourth grade math scores, however, public school students performed better–even after controlling for the fact that different types of student attend public schools and private schools.

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The Monty Hall problem is a statistical puzzle loosely based on the game show Let’s Make a Deal, which was hosted by Monty Hall. Many websites discuss the Monty Hall problem, but the crux of the idea is that you are looking to win a prize that can be found behind one of three doors. The way the game works is this: You pick door number one, two, or three. The host, Monty Hall, then picks one of the other two doors that you did not pick, and tells you that there is no prize behind that door. He then offers you the chance to switch your choice or keep your original choice.

For example, if you pick door number one, Monty will tell you that the prize is NOT behind door number two. He then offers you the choice of sticking with door number one or switching to door number three. The crux of the statistical problem is whether it is a better choice to switch, to keep the same door, or that it does not matter. The seemingly intuitive answer is that it does not matter. The prize is either behind door one or door three, and you have no idea which one it is, so your chances are fifty-fifty.

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Bill Tancer from Hitwise has created an interesting application using their data. You can read his post here. His thinking was that people are increasingly likely to use online methods to file for unemployment. He then tracks the search term “unemployment” as well as collects data from state unemployment websites. Since Hitwise collects this information on a daily basis, and th US Department of Labor realeases the official statistics with la lag of a few days, Tancer can use the Hitwise data to predict the change in unemployment rates before they are announced. Even though the model is, by the author’s admission, in the early stages, I think this is a novel way of using inexpensive data to increase the speed of unemployment predictions.