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:

Scatter Plot 450 400 350 300 250 Yards/Game 2i) 150 100 50 tD 10 15 20 25 30 35 40 Points/Game

There seems to be a positive linear relationship.

b.

The regression model is:

Y--19.24775626504550.125889132361051 * X

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.

Yards/Game Residual Plot 50 100 150 200250300 350 400 450 -2 -4 -6 Yards/Game

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

1 SUMMARY OUTPUT 2 Normal Probability Plot Regression Statistics 40 4 Multiple R 5 R Square 6 Adjusted R Square 7 Standard Error 8 Observations 0.894399656 0.799950744 0.793282436 2.269815014 32 20 2 0 20460 80 100 120 Sample Percentile 10 ANOVA MS 618.0569441 119.9630673 5.152060197 Significance F 1 618.0569441 30 154.5618059 772.61875 5.27168E-12 12 Regression 13 Residual 14 Total 15 16 17 Intercept 18 Yards/Game 19 20 P-value Coefficients Standard Error 19.247756273.759480472 0.011493822 per 95% Lower 95.0% uper 95.0% 26.92563966-11.56987287-26.92563966-11.56987287 0.102415617 0.149362648 0.102415617 0.149362648 t Stat Lower 95% 5.119791526 1.661E-05 10.95276528 5.27168E-12 0.125889132

Here is the residual output:

2RESIDUAL OUTPUT PROBABILITY OUTPUT Predicted Points/Game Residuals Standard Residuals Percen 1.5625 4.6875 7.8125 10.9375 14.0625 17.1875 20.3125 23.4375 26.5625 29.6875 32.8125 35.937 39.0625 42.1875 45.3125 48.4375 51.5625 54.6875 57.8125 60.9375 64.0625 67.1875 70.3125 73.4375 76.5625 79.6875 82.8125 85.9375 89.0625 92.1875 95.3125 98.4375 24.07069418 1.12930582 18.64487258 -2.444872576 18.77076171 -1.570761708 15.6361223 0.163877688 16.61805754 0.081942455 17.66293734 3.237062657 24.5616618 -0.761661797 24.97709593 0.122904067 26.789899441.610100561 24.34765027 -4.347650272 21.40184457 0.198155426 27.4193451 0.219345101 22.74885829 0.951141709 25.90867551 2.191324487 25.74501964 -0.045019641 15.59835557 -1.498355572 16.94536929-0.245369289 23.07617003 -0.276170035 32.51785496 4.282145038 26.22339834 -2.523398344 22.4719022 0.828097801 17.85177104 -1.051771042 17.86435995 -0.164359955 25.83314203 -4.833142033 21.96834567 2.63165433 20.43249826 5.367501745 10.625734843.074265156 24.67496202 0.074962016 18.20426061 1.804260612 21.89281219 -0.992812191 19.99188629 -1.191886292 22.72368046 1.823680464 0.505756323 1.094929065 0.703461058 0073392145 0.03669769 1.449709086 0.341108018 0.055042228 0.721078848 1.947082516 0.08874333 0.098233065 0.425966045 0.981378292 -0.020161915 0.671034181 0.109887922 -0.123681946 1.917746188 Yards/Game Residual Plot 16.2 16.4 10 6 100 16.7 10 18.8 20 12 Yards/Game Line Fit Plot 15 20 0.370861189 0.471032599 0.073608127 2.164508588 1.17857873 2.403820029 1.376800699 0.03357152 0.808032862 0.444628049 -0.533782806 0.816729986 23.8 25.2

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