Calculate the least squares estimates of the slope and intercept. What is the estimate of 2? Graph the regression model. (b) Find an estimate of the mean number of games won if the opponents can be limited to 1800 yards rushing. (c) What change in the expected number of games won is associated with a decrease of 100 yards rushing

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Solve the following statistical problems using regression analysis.

PROBLEM: Montgomery, Peck, and Vining (2001) present data concerning the performance of the 28 National Football League teams in 1976. It is suspected that the number of games won (y) is related to the number of yards gained rushing by an opponent (x). The data are shown in the following table.

(a) Calculate the least squares estimates of the slope and intercept. What is the estimate of 2? Graph the regression model.
(b) Find an estimate of the mean number of games won if the opponents can be limited to 1800 yards rushing.
(c) What change in the expected number of games won is associated with a decrease of 100 yards rushing by an opponent?

Yards
Yards
Rushing by
Opponent (x)
Rushing by
Opponent (x)
Games
Games
Teams
Won (y)
Teams
Won (y)
Washington
10
2205
Detroit
6.
1901
Minnesota
11
2096
Green Bay
2288
New England
11
1847
Houston
2072
Oakland
13
1903
Kansas City
5
2861
Pittsburgh
10
1457
Miami
6.
2411
Baltimore
11
1848
New Orleans
4
2289
Los Angeles
10
1564
New York Giants
3
2203
Dallas
11
1821
New York Jets
3
2592
Atlanta
4
2577
Philadelphia
4
2053
St. Louis
San Diego
Buffalo
2476
10
1979
Chicago
7
1984
6.
2048
Cincinnati
10
1917
San Francisco
8
1786
Cleveland
1761
Seattle
2
2876
Denver
9.
1709
Tampa Bay
2560
Transcribed Image Text:Yards Yards Rushing by Opponent (x) Rushing by Opponent (x) Games Games Teams Won (y) Teams Won (y) Washington 10 2205 Detroit 6. 1901 Minnesota 11 2096 Green Bay 2288 New England 11 1847 Houston 2072 Oakland 13 1903 Kansas City 5 2861 Pittsburgh 10 1457 Miami 6. 2411 Baltimore 11 1848 New Orleans 4 2289 Los Angeles 10 1564 New York Giants 3 2203 Dallas 11 1821 New York Jets 3 2592 Atlanta 4 2577 Philadelphia 4 2053 St. Louis San Diego Buffalo 2476 10 1979 Chicago 7 1984 6. 2048 Cincinnati 10 1917 San Francisco 8 1786 Cleveland 1761 Seattle 2 2876 Denver 9. 1709 Tampa Bay 2560
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