It is thought that prehistoric Indians did not take their best tools, pottery, and household items...

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It is thought that prehistoric Indians did not take their besttools, pottery, and household items when they visited higherelevations for their summer camps. It is hypothesized thatarchaeological sites tend to lose their cultural identity andspecific cultural affiliation as the elevation of the siteincreases. Let x be the elevation (in thousands of feet) for anarchaeological site in the southwestern United States. Let y be thepercentage of unidentified artifacts (no specific culturalaffiliation) at a given elevation. Suppose that the following datawere obtained for a collection of archaeological sites in NewMexico: x 5.50 6.25 6.75 7.25 7.50 y 9 38 38 50 72 What percentageof the variation in y can be explained by the correspondingvariation in x and the least-squares line?
Select one:
a. 89.9%
b. 10.1%
c. 94.8%
d. 0.3%
e. 1.0%

Answer & Explanation Solved by verified expert

4.2 Ratings (541 Votes)

X	Y	(x-x?)²	(y-y?)²	(x-x?)(y-y?)
5.5	9	1.3225	1049.76	37.26
6.25	38	0.16	11.56	1.36
6.75	38	0.01	11.56	-0.34
7.25	50	0.36	73.96	5.16
7.5	72	0.7225	936.36	26.01

	?X	?Y	?(x-x?)²	?(y-y?)²	?(x-x?)(y-y?)
total sum	33.25	207	2.575	2083.2	69.45
mean	6.65	41.4	SSxx	SSyy	SSxy

sample size ,   n =   5
here, x? =   6.65       y? =   41.4

SSxx =    ?(x-x?)² =    2.575
SSxy=   ?(x-x?)(y-y?) =   69.45
R² =    (Sxy)²/(Sx.Sy) =    0.8992

so, 89.92 %variation in y can be explained by the corresponding variation in x and the least-squares line

option a) is answer

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