Math 314 Section 3 Project #2 Due: 11/13/98 As background material read the Least Squares subsection on pages 143-146 and the project on page 169 of your textbook. This projects is very similar, but the data is different. The Big Twelve needs your help! Your job is to create a model that predicts scores in football games. First, you will need to collect the data for this project, which consists of past game scores up to the dates indicated in the questions below. Set this data up in a table similar to that of page 169. You should be able to find this data on the Web. Go to various sports sites; each University will have their own. Then follow the instructions below to set up in Maple a system that represents each game as an equation. Use least squares to solve the system. The resulting power ratings are a basis for predictions. Use these ratings to answer these questions: 1. Based on the ratings prior to November 7, what point spreads would you predict for each of the Big 12 games scheduled for that day? 2. How accurate were your predictions? 3. Based on all available Big 12 data prior to November 13, what team do you predict will win the Big 12 title? You may modify the model with your own biases, as long as they can be quantified. However, you should not use this separate model to answer questions 1-3. Implementation Notes: The basic idea is fairly simple. Index the teams as teams 1 to12. Now assign each team a power rating xi. Ideally, the difference xi- xj should represent the "point spread" of the game in which team i plays team j. That is, team i's score minus team j's score should be xi- xj. Suppose team 1 played 3 with a resulting score of 24 (for 1) and 14 (for 2). Then the linear equation that results is x1- x2 = 24 - 14 = 10. Thus, if we have 36 games, then the resulting system is 36 equations in 12 unknowns. This system will almost certainly be inconsistent, so we need to use least squares to solve the system. One minor technical point: The system as given has a coefficient matrix of less than full column rank (use Maple to verify this). Remedy this difficulty by setting one of the teams power rating at 100. Make it the top team in your rating (you'll have to experiment). The extra equation will look something like: x5 = 100. Now set up the normal equations and solve them with Maple.