Question

# The table below shows the number of interceptions thrown during the season by seven randomly selected...

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:

0.53

-67.82

67.82

-0.53

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

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