Denise Lau is an avid football fan and religiously follows every game of the National Football League. During the 2017 season, she meticulously keeps a record of how each quarterback has played throughout the season. Denise is making a presentation at the local NFL fan club about these quarterbacks. The accompanying table shows a portion of the data that Denise has recorded with the following variables: the players name (Player), teams name (Team), completed passes (Comp), attempted pass (Att), completion percentage (Pct), total yards thrown (Yds), average yards per attempt (Avg), yards thrown per game (Yds/G), number of touchdowns (TD), and number of interceptions (Int).

Player	Team	Comp	Att	Pct	Yds	Avg	Yds/G	TD	Int
Aaron Rodgers	GB	154	238	64.7	1675	7	239.3	16	6
Alex Smith	KC	341	505	67.5	4042	8	269.5	26	5
Andy Dalton	CIN	297	496	59.9	3320	6.7	207.5	25	12
Ben Roethlisberger	PIT	360	561	64.2	4251	7.6	283.4	28	14
Blaine Gabbert	ARI	95	171	55.6	1086	6.4	217.2	6	6
Blake Bortles	JAX	315	523	60.2	3687	7	230.4	21	13
Brett Hundley	GB	192	316	60.8	1836	5.8	166.9	9	12
Brock Osweiler	DEN	96	172	55.8	1088	6.3	181.3	5	5
Bryce Petty	NYJ	55	112	49.1	544	4.9	136	1	3
C.J. Beathard	SF	123	224	54.9	1430	6.4	204.3	4	6
Cam Newton	CAR	291	492	59.1	3302	6.7	206.4	22	16
Carson Palmer	ARI	164	267	61.4	1978	7.4	282.6	9	7
Carson Wentz	PHI	265	440	60.2	3296	7.5	253.5	33	7
Case Keenum	MIN	325	481	67.6	3547	7.4	236.5	22	7
Dak Prescott	DAL	308	490	62.9	3324	6.8	207.8	22	13
Derek Carr	OAK	323	515	62.7	3496	6.8	233.1	22	13
Deshaun Watson	HOU	126	204	61.8	1699	8.3	242.7	19	8
DeShone Kizer	CLE	255	476	53.6	2894	6.1	192.9	11	22
Drew Brees	NO	386	536	72	4334	8.1	270.9	23	8
Drew Stanton	ARI	79	159	49.7	894	5.6	178.8	6	5
Eli Manning	NYG	352	571	61.6	3468	6.1	231.2	19	13
Jacoby Brissett	IND	276	469	58.8	3098	6.6	193.6	13	7
Jameis Winston	TB	282	442	63.8	3504	7.9	269.5	19	11
Jared Goff	LA	296	477	62.1	3804	8	253.6	28	7
Jay Cutler	MIA	266	429	62	2666	6.2	190.4	19	14
Jimmy Garoppolo	SF	120	178	67.4	1560	8.8	260	7	5
Joe Flacco	BAL	352	549	64.1	3141	5.7	196.3	18	13
Josh McCown	NYJ	267	397	67.3	2926	7.4	225.1	18	9
Kirk Cousins	WAS	347	540	64.3	4093	7.6	255.8	27	13
Marcus Mariota	TEN	281	453	62	3232	7.1	215.5	13	15
Matt Moore	MIA	78	127	61.4	861	6.8	215.2	4	5
Matt Ryan	ATL	342	529	64.7	4095	7.7	255.9	20	12
Matthew Stafford	DET	371	565	65.7	4446	7.9	277.9	29	10
Mike Glennon	CHI	93	140	66.4	833	6	208.2	4	5
Mitchell Trubisky	CHI	196	330	59.4	2193	6.6	182.8	7	7
Nick Foles	PHI	57	101	56.4	537	5.3	76.7	5	2
Philip Rivers	LAC	360	575	62.6	4515	7.9	282.2	28	10
Russell Wilson	SEA	339	553	61.3	3983	7.2	248.9	34	11
Ryan Fitzpatrick	TB	96	163	58.9	1103	6.8	183.8	7	3
Tom Brady	NE	385	581	66.3	4577	7.9	286.1	32	8
Tom Savage	HOU	125	223	56.1	1412	6.3	176.5	5	6
Trevor Siemian	DEN	206	349	59	2285	6.5	207.7	12	14
Tyrod Taylor	BUF	263	420	62.6	2799	6.7	186.6	14	4

a. Conduct principal component analysis on all the numerical variables in the data set. Should you use the covariance matrix or the correlation matrix for the analysis in this case?

multiple choice

• Use the covariance matrix because the variables have different scales

• Use the covariance matrix because the variables have the same scale

• Use the correlation matrix because the variables have different scales

• Use the correlation matrix because the variables have the same scale

b. Allow the maximum number of principal components to be calculated by the software. How many principal components are computed? What percent of the total variability is accounted for by the first three principal components? How many principal components must be retained in order to account for at least 80% of the total variance in the data? (Show your final answer as a percentage point with 2 decimal places.)

Number of principal components
Percentage of total variability		%
Components retained for atleast 80% of total variance

c. Which original variable is given the highest weight to compute the first principal component? Which original variable is given the highest weight to compute the second principal component?

	was given the most weight to compute the first principal component.
	was given the most weight to compute the second principal component. d. What is the principal component 1 score for the first record (Aaron Rodgers)? (Round your final answer to 4 decimal places.)

The first record (Aaron Rodgers) had a score of

for the first principal component.

*****all data from table is included,,, nothing else to add ******