Question

1. The excel file National Football League provides various data on professional football for one season.    

1. Construct a scatter diagram for Points/Game and Yards/Game in the Excel file. Does there appear to be a linear relationship?
2. Develop a regression model for predicting Points/Game as a function of Yards/Game. Explain the statistical significance of the model.
3. Draw conclusions about the validity of the regression analysis assumptions from the residual plot and standard residuals.

National Football League Data 2007 Season
Team	Points/Game	Yards/Game	Rushing Yards/Game	Passing Yards/Game	Opponent Yards/Game	Opponent Rushing Yards/Game	Opponent Passing Yards/Game	Penalties	Penalty Yards	Interceptions	Fumbles	Passes Intercepted	Fumbles Recovered
Arizona Cardinals	25.2	344.1	90	254.1	330.2	97.9	232.3	137	1,128	18	11	24	12
Atlanta Falcons	16.2	301	95	206	355.5	127.1	228.4	105	891	16	12	15	9
Baltimore Ravens	17.2	302	112.3	189.7	301.6	79.3	222.3	107	873	17	6	14	26
Buffalo Bills	15.8	277.1	112.5	164.6	362.9	124.6	238.4	78	633	18	12	14	7
Carolina Panthers	16.7	284.9	114	170.9	324.8	110.7	214.1	95	801	14	16	17	12
Chicago Bears	20.9	293.2	83.1	210.1	354.7	122.9	231.8	111	839	16	17	21	13
Cincinnati Bengals	23.8	348	97.3	250.8	348.8	118.3	230.4	90	670	19	16	20	10
Cleveland Browns	25.1	351.3	118.4	232.9	359.6	129.5	230.1	114	868	17	10	20	9
Dallas Cowboys	28.4	365.7	109.1	256.6	307.6	94.6	213.1	104	815	19	10	19	5
Denver Broncos	20	346.3	122.3	224	336	142.6	193.4	90	610	14	16	15	14
Detroit Lions	21.6	322.9	80.5	242.4	377.6	119.4	258.2	100	676	17	18	22	14
Green Bay Packers	27.2	370.7	99.8	270.9	313.3	102.9	210.4	113	1,006	19	9	15	9
Houston Texans	23.7	333.6	99.1	234.4	344.2	114.1	230.1	82	636	11	14	21	17
Indianapolis Colts	28.1	358.7	106.6	252.1	279.7	106.9	172.8	67	515	22	15	14	5
Jacksonville Jaguars	25.7	357.4	149.4	208	313.8	100.3	213.5	76	594	20	10	8	13
Kansas City Chiefs	14.1	276.8	78	198.8	319.4	130.6	188.9	101	697	14	8	20	13
Miami Dolphins	16.7	287.5	98.1	189.4	342.2	153.5	188.7	91	732	14	8	16	13
Minnesota Vikings	22.8	336.2	164.6	171.6	338.1	74.1	264.1	86	662	15	16	14	16
New England Patriots	36.8	411.2	115.6	295.7	288.3	98.3	190.1	78	690	19	12	9	6
New Orleans Saints	23.7	361.2	91.6	269.6	348.1	102.9	245.3	68	581	13	10	18	12
New York Giants	23.3	331.4	134.3	197.1	305	97.7	207.3	77	652	15	10	20	14
New York Jets	16.8	294.7	106.3	188.4	331.9	134.8	197.1	63	486	15	6	19	6
Oakland Raiders	17.7	294.8	130.4	164.4	341.6	145.9	195.8	120	864	18	8	20	17
Philadelphia Eagles	21	358.1	123.4	234.7	311.4	95.8	215.6	83	649	11	8	15	12
Pittsburgh Steelers	24.6	327.4	135.5	191.9	266.4	89.9	176.5	80	651	11	14	14	8
San Diego Chargers	25.8	315.2	127.4	187.8	320.3	107	213.3	94	761	30	18	16	8
San Francisco 49ers	13.7	237.3	92.3	145	346.2	118.5	227.7	97	702	12	10	17	17
Seattle Seahawks	24.6	348.9	101.2	247.8	321.8	102.8	219.1	59	428	20	14	13	11
St. Louis Rams	16.4	297.5	95.4	202.1	341.1	115.3	225.8	94	794	18	9	28	9
Tampa Bay Buccaneers	20.9	326.8	117	209.8	278.4	107.9	170.5	81	614	16	19	8	12
Tennessee Titans	18.8	311.7	131.8	179.9	291.6	92.4	199.2	101	773	22	12	17	17
Washington Redskins	20.9	333.4	116.9	216.4	305.3	91.3	214	90	751	14	10	11	18

Answer 1

a.

The scatter plot is given by:

There seems to be a positive linear relationship.

b.

The regression model is:

Where X is the Yards/Game and Y is predicted Points/Game.

c.

validity of the regression analysis assumptions from the residual plot and standard residuals.

The residual plot and standard residual are randomly spread out all over the graph, which means that they are not following any particular pattern at all. So the linear model is a good fit for this data since the residuals are spread out in randomness.

Go to Data -> Data Analysis-> Regression to run the model in excel:

Here is the residual output:

Let me know in comments if anything is unclear. Will reply ASAP. Please upvote!