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Suppose you are a rabid football fan and you get into a discussion about the importance of offense (yards made) versus defense (yards allowed) in...
Suppose you are a rabid football fan and you get into a discussion about the importance of offense (yards made) versus defense (yards allowed) in terms of winning a game. You decide to look at football statistics to provide evidence of which variable is a stronger predictor of wins.
Part a) Develop a simple linear regression that compares wins to yards made. Perform the following diagnostics on this regression: 1) test of significance on the slope; 2) assess the fit of the line using the appropriate statistics; 3) interpret the slope of the equation if the slope is significant. Part b) Develop a simple linear regression that compares wins against yards allowed. Perform the following diagnostics on this regression: 1) test of significance on the slope; 2) assess the fit of the line using the appropriate statistics; 3) interpret the slope of the equation if the slope is significant. Part c) Which explanatory variable provides a better prediction of the response variable? Support your answer briefly by citing the appropriate diagnostics. Note: Use an alpha of .05 for both tests of significance. Be sure to show ALL steps of the hypothesis testing procedure.
There is the same data (Excel style):
Team
Win
Rush
Pass
Yds Allowed
Yds Made
Arizona Cardinals
62.50
93.40
251.00
346.40
344.40
Atlanta Falcons
56.30
117.21
223.19
348.90
340.40
Baltimore Ravens
56.30
137.51
213.69
305.00
351.20
Buffalo Bills
37.50
116.71
157.19
340.60
273.90
Carolina Panthers
50.00
156.16
174.94
315.80
331.10
Chicago Bears
43.80
93.24
217.06
337.80
310.30
Cincinnati Bengals
62.50
128.48
180.63
301.40
309.10
Cleveland Browns
31.30
130.45
129.75
389.30
260.20
Dallas Cowboys
68.80
131.46
267.94
315.90
399.40
Denver Broncos
50.00
114.71
226.69
315.00
341.40
Detroit Lions
12.50
101.00
198.00
392.10
299.00
Green Bay Packers
68.80
117.85
261.25
284.40
379.10
Houston Texans
56.30
92.23
290.88
324.90
383.10
Indianapolis Colts
87.50
80.91
282.19
339.20
363.10
Jacksonville Jaguars
53.80
126.85
209.75
352.30
336.60
Kansas City Chiefs
25.00
120.58
182.63
388.20
303.20
Miami Dolphins
43.80
139.48
198.13
349.30
337.60
Minnesota Vikings
75.00
119.85
259.75
305.50
379.60
New England Patriots
62.50
120.05
277.25
320.20
397.30
New Orleans Saints
81.30
131.61
272.19
357.80
403.80
New York Giants
50.00
114.81
251.19
324.90
366.00
New York Jets
56.30
172.25
148.75
252.30
321.00
Oakland Raiders
31.30
106.29
159.81
361.90
266.10
Philadelphia Eagles
68.80
102.34
255.56
321.10
357.90
Pittsburgh Steelers
56.30
112.05
259.25
305.30
371.30
Saint Louis Rams
6.30
111.50
167.88
327.00
279.38
San Diego Chargers
81.30
88.94
271.13
326.40
360.06