a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 4BGP
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Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information:

x 1 2 3 4 5
y 15.8 18.1 14.4 19.6 20.0
 
Σx = 15; Σy = 87.9; Σx2 = 55; Σy2 = 1,568.77; Σxy = 273.6
(a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.)
x
y
b
ŷ +  x
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Follow-up Question

(c) Find the sample correlation coefficient r and the coefficient of determination r2. (Round your answers to three decimal places.)

r =  
r2 =  


What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)

 

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Follow-up Question

Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram.

 

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