It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) of an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. The following data were obtained for a collection of archaeological sites in New Mexico. x 5.35 Y| 18 7.25 5.67 12 6.25 33 6.75 37 62 A USE SALT Complete parts (a) through (e), given Ex = 31.27, Ey = 162, Ex² = 197.9589, Ey² = 6770, Exy = 1069.84, and r= 0.9390. (c) Find x, and y. Then find the equation of the least-squares line ŷ= a + bx. (Round your answer to four decimal places.) (d) (e) Find the value of the coefficient of determination 2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to four decimal places. Round your answers for the percentages to two decimal place.) explained unexplained (f) At an archaeological site with elevation 6.4 (thousand feet), what does the least-squares equation forecast for y = percentage of culturally unidentified artifacts? (Round your answer to two decimal places.)
It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) of an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. The following data were obtained for a collection of archaeological sites in New Mexico. x 5.35 Y| 18 7.25 5.67 12 6.25 33 6.75 37 62 A USE SALT Complete parts (a) through (e), given Ex = 31.27, Ey = 162, Ex² = 197.9589, Ey² = 6770, Exy = 1069.84, and r= 0.9390. (c) Find x, and y. Then find the equation of the least-squares line ŷ= a + bx. (Round your answer to four decimal places.) (d) (e) Find the value of the coefficient of determination 2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to four decimal places. Round your answers for the percentages to two decimal place.) explained unexplained (f) At an archaeological site with elevation 6.4 (thousand feet), what does the least-squares equation forecast for y = percentage of culturally unidentified artifacts? (Round your answer to two decimal places.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 32PPS
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Transcribed Image Text:9.
It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that
archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) of an
archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. The following data were
obtained for a collection of archaeological sites in New Mexico.
5.35
18
5.67
6.25
6.75
7.25
y
12
33
37
62
n USE SALT
Complete parts (a) through (e), given Ex = 31.27, Ey = 162, Ex² = 197.9589, Ey² = 6770, Exy = 1069.84, and r= 0.9390.
(c) Find x, and y. Then find the equation of the least-squares line ŷ= a + bx. (Round your
answer to four decimal places.)
(d)
(e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line?
What percentage is unexplained? (Round your answer for r2 to four decimal places. Round your answers for the percentages to two decimal place.)
r2 =
explained
%
unexplained
%
(f) At an archaeological site with elevation 6.4 (thousand feet), what does the least-squares equation forecast for y = percentage of culturally unidentified artifacts? (Round
your answer to two decimal places.)
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