- First Part:
- Demonstrate how the method works by using it to find the best fit line (called a linear regression line) through the following three points: A=(0,0), B=(1,1), C=(2,1). (I.e., write a system of equations that m and b would have to satisfy if y = mx + b were to be the equation of a line through these three points. Since the points do not lie on a line, your system of equations will be inconsistent, but you can still get a best fit line using the method described above.)
- Go to the library and get the formula for the linear regression line from a stat book (cite your reference), and get the equation of the line using the formula. Put the formula in your project write up, and compare what it gives you with what you got by the matrix method. (Note: most calculators can do linear regression.)

- Second Part:
- For the second part, we want to predict the difference in scores
when any two teams of the North Division of the Big Twelve play
each other. It seems reasonable to assume that stronger
teams will beat weaker teams, and that the stronger a team is
the more it will win by. So we want to assign a number, call it a
power rating, to each of the teams in the Big Twelve North such that
if team A has a power rating of p
_{A}and team B has a power rating of p_{B}, then when team A plays team B, the difference in the scores should be the difference, p_{A}- p_{B}. - So, for each game played before November 13 between any
two teams A and B of the Big Twelve North, write down an equation
of the form p
_{A}- p_{B}= d_{AB}, where d_{AB}is the actual difference in scores of that game. The power ratings are the unknowns which you will try to solve for. - Since by November 13 there will have been 12 games played between
the 6 North Division teams, you will have a system of
12 equations in 6 unknowns.
- Between November 13 and November 18, find the best possible solution to the system of equations.
- Use your solution to predict the score differential, and hence the winner, of the Colorado/Nebraska game.
- Also, determine what prediction this method of least squares gives for the outcome of the Kansas State/Nebraska game November 12, based on North Division games played before November 12, and discuss how well you feel the method worked.

- For the second part, we want to predict the difference in scores
when any two teams of the North Division of the Big Twelve play
each other. It seems reasonable to assume that stronger
teams will beat weaker teams, and that the stronger a team is
the more it will win by. So we want to assign a number, call it a
power rating, to each of the teams in the Big Twelve North such that
if team A has a power rating of p

- An introduction where you briefly explain that you are demonstrating how to apply least squares to make predictions. (Aside: the first use of least squares was by C. F. Gauss, regarding astronomical orbital predictions.)
- Use part I as an example of the method.
- For part II, separately for the Colorado/Nebraska and the Kansas State/Nebraska games, state whether the system is consistent or inconsistent. Discuss why you might or might not expect this system to be consistent.
- Include enough of the main steps so that I can check how you found your least squares solutions for each of the two games.
- Be sure to include an explicit prediction of which team will win the Colorado/Nebraska game, and by how much.
- Discuss why you think the Kansas State/Nebraska game prediction did or did not work well, taking into account the actual outcome of the game.