14. (4.50 S AQ) One of nature\'s patterns connects the percent of adult birds in

Question

14. (4.50 S AQ) One of nature's patterns connects the percent of adult birds in a colony that returm from the previous year and the number of new adults that join the colony. Following are data for 13 colonies of sparrowhawks Percent return 75 62 82 52 69 58 49 41 60 51 59 51 43 New adults 3 6 10 12 13 16 16 15 20 19 20 19 19 Use your calculator or software to find the correlation (+ 0.001) between the percent of returming birds and the number of new birds: Below is the scatterplot of the original data (green) and two new points added. Point A (blue): 9% return, 25 new birds. Point B (red): 37% return, 6 new birds. Find the new correlation (± 0.001) for the original data plus Point A Find the new correlation (± 0.001) for the original data plus Point B Adding point A makes correlation

Explanation / Answer

X Values
= 752
Mean = 57.846
(X - Mx)2 = SSx = 1735.692

Y Values
= 188
Mean = 14.462
(Y - My)2 = SSy = 359.231

X and Y Combined
N = 13
(X - Mx)(Y - My) = -475.077

R Calculation
r = ((X - My)(Y - Mx)) / ((SSx)(SSy))

r = -475.077 / ((1735.692)(359.231)) = -0.602

Adding Point A

r = --0.7051, Makes corr. stronger

Adding point B

r= -0.3262 , Makes corr. Weaker

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