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 14.2 17.7 14.4 19.6 20.0 Σx = 15; Σy = 85.9; Σx2 = 55; Σy2 = 1,506.45; Σxy = 271.2 (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 (b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram. (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.) %

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 14.2 17.7 14.4 19.6 20.0 Σx = 15; Σy = 85.9; Σx2 = 55; Σy2 = 1,506.45; Σxy = 271.2 (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 (b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram. (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.) %

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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Question

x	1	2	3	4	5
y	14.2	17.7	14.4	19.6	20.0

Σx = 15; Σy = 85.9; Σx² = 55; Σy² = 1,506.45; Σxy = 271.2

(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

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

(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.)
%

Definition Definition Relationship between two independent variables. A correlation tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

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