Question

The table below shows the number of interceptions thrown during the season by seven randomly selected National Football League teams and the number of games those teams won during the season.

Wins	Interceptions
2	20
5	18
10	15
13	6
10	8
8	24
8	10

Find the correlation coefficient for this data:

Group of answer choices

0.53

-67.82

67.82

-0.53

Answer 1

n = 7

The last row represent the total of each coloumn

Wins (x)	Interceptions (y)	x*x	y*y	xy
2	20	4	400	40
5	18	25	324	90
10	15	100	225	150
13	6	169	36	78
10	8	100	64	80
8	24	64	576	192
8	10	64	100	80
56	101	526	1725	710

r = [n* total of xy - (total of x) * ( total of y)]/ underroot [(n* total of x*x) -( total of x)2] * [(n* total of y*y) -( total of y)2

solving the numerator = 7*710 - (56*101) = 4970 - 5656 = - 686

Solving the denominator = underrrot(7*526)-(56)2 * (7*1725)-(101)2 = [3682 - 3136 ] * [12075-10201]

= 546 * 1874 = underroot 1023204 = 1011.535

r = -686/1011.535 = -0.67817

so coefficient of correlation = -0.67817 * 100 = -67.82