One of nature's patterns connects the percent of adult birds in a colony that return from the previous year and the number of new adults that join the colony. Here are data for 10 colonies of sparrowhawks: Percent return, X 74 66 81 52 52 16 73 62 45 17 62 18 46 New adults, Y 6 11 12 15 18 (a) Draw a scatter plot of the data. (b) Find the equation of the least squares regression line for predicting y from x using the information below: Σ-613 , Σ-38959, Σ у, 3D 126, Уу- = 1808, x,y, = 7333 n=10 = = (Show the details of your work.) X denotes the percent of adult sparrowhawks that return to a colony from the previous year, and Y denotes the number of new adult birds that join the colony.

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One of nature's patterns connects the percent of adult birds in a colony that return
from the previous year and the number of new adults that join the colony. Here are data for 10
colonies of sparrowhawks:
81
Percent return, X
New adults, Y
74
6
66
52
73
62
52
12
15
16
45
17
62
18
46
18
11
(a) Draw a scatter plot of the data.
(b) Find the equation of the least squares regression line for predicting y from x using the
information below:
n=10 >x, = 613 ,
Ex = 38959, Ey;
= 126, Ey = 1808, Ex,y; = 7333
(Show the details of your work.)
X denotes the percent of adult sparrowhawks that return to a colony from the previous year, and
Y denotes the number of new adult birds that join the colony.
Transcribed Image Text:One of nature's patterns connects the percent of adult birds in a colony that return from the previous year and the number of new adults that join the colony. Here are data for 10 colonies of sparrowhawks: 81 Percent return, X New adults, Y 74 6 66 52 73 62 52 12 15 16 45 17 62 18 46 18 11 (a) Draw a scatter plot of the data. (b) Find the equation of the least squares regression line for predicting y from x using the information below: n=10 >x, = 613 , Ex = 38959, Ey; = 126, Ey = 1808, Ex,y; = 7333 (Show the details of your work.) X denotes the percent of adult sparrowhawks that return to a colony from the previous year, and Y denotes the number of new adult birds that join the colony.
(c) An ecologist uses this regression line to predict how many birds will join another colony when
50 percent of the adults from the previous year return. What is the prediction?
(d) An ecologist uses this regression line to predict how many birds will join another colony when
95 percent of the adults from the previous year return. What is the prediction? Comment on the
appropriateness of using the line in (b) for this prediction.
(e) Calculate the correlation coefficient between X and Y. (Show details of your work.)
Transcribed Image Text:(c) An ecologist uses this regression line to predict how many birds will join another colony when 50 percent of the adults from the previous year return. What is the prediction? (d) An ecologist uses this regression line to predict how many birds will join another colony when 95 percent of the adults from the previous year return. What is the prediction? Comment on the appropriateness of using the line in (b) for this prediction. (e) Calculate the correlation coefficient between X and Y. (Show details of your work.)
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