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Now use the Massey Method with a 10 max point differential for the following system: During the Early Part of the Season: Team B beats C by 8 points. Team D beats E by 5 points. During the Middle Part of the Season: Team A beats D by 10 points. Team E beats C by 5 points. During the Later Part of the Season: Team A beats E by 4. Team E beats B by 20 points. a. Draw a directed graph of this season. b. Write the system of equations for this season using the Massey method. c. Solve the system (using least squares) to find the ratings for each team, and use those ratings to rank them.

Now use the Massey Method with a 10 max point differential for the following system: During the Early Part of the Season: Team B beats C by 8 points. Team D beats E by 5 points. During the Middle Part of the Season: Team A beats D by 10 points. Team E beats C by 5 points. During the Later Part of the Season: Team A beats E by 4. Team E beats B by 20 points. a. Draw a directed graph of this season. b. Write the system of equations for this season using the Massey method. c. Solve the system (using least squares) to find the ratings for each team, and use those ratings to rank them.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Need help with Linear Algebra,the image is a similar example for it.

Now use the Massey Method with a 10 max point differential for the following system:
During the Early Part of the Season: Team B beats C by 8 points. Team D beats E by 5 points.
During the Middle Part of the Season: Team A beats D by 10 points. Team E beats C by 5 points.
During the Later Part of the Season: Team A beats E by 4. Team E beats B by 20 points.

a. Draw a directed graph of this season.

b. Write the system of equations for this season using the Massey method.

c. Solve the system (using least squares) to find the ratings for each team, and use those ratings to rank them.

3.2.3 A Way to Use Scores - The Massey System of Ranking Suppose we want to use a system of rating that incorporates the scores of the games. On the other hand, Kenneth Massey's method of sports rating creates a system of equations which is based on the score of the games played. Massey originally created this method for ranking college football teams. Using the Massey Method, for each game, the difference in the ratings correlates to the point differential. This is represented as a system: r₁ rj = bk where r, is the rating for team i and r, is the rating for team j and bk is the score differential for game k. Example 3.3. Suppose I have 3 teams, A, B, and C. Suppose Team A beat Team B by 7, Team C beat Team A by 1, Team C beat team B by 1, and Team B beat Team C by 10, we would get the following system of equations: ΤΑ TB = 7 TC-TA = 1 rc - TB: = 1 TBTC = 10 Which will give us the following matrix system, Xr = b: -1 0 TA DE TB ra 0 1 10 Note that each row of our system of equations representing a particular game from the data set. Our columns represent the different teams being ranked. This usually means in practice that our system has more rows than columns.
Transcribed Image Text:3.2.3 A Way to Use Scores - The Massey System of Ranking Suppose we want to use a system of rating that incorporates the scores of the games. On the other hand, Kenneth Massey's method of sports rating creates a system of equations which is based on the score of the games played. Massey originally created this method for ranking college football teams. Using the Massey Method, for each game, the difference in the ratings correlates to the point differential. This is represented as a system: r₁ rj = bk where r, is the rating for team i and r, is the rating for team j and bk is the score differential for game k. Example 3.3. Suppose I have 3 teams, A, B, and C. Suppose Team A beat Team B by 7, Team C beat Team A by 1, Team C beat team B by 1, and Team B beat Team C by 10, we would get the following system of equations: ΤΑ TB = 7 TC-TA = 1 rc - TB: = 1 TBTC = 10 Which will give us the following matrix system, Xr = b: -1 0 TA DE TB ra 0 1 10 Note that each row of our system of equations representing a particular game from the data set. Our columns represent the different teams being ranked. This usually means in practice that our system has more rows than columns.
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