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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: 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.

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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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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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