# statistics

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 5.19 5.83 6.25 6.75 7.25
y 18 13 33 37 62
Complete parts (a) through (e), given Σx = 31.27, Σy = 163, Σx2 = 198.1125, Σy2 = 6795, Σxy = 1074.71, and r ≈ 0.900.
(a) Draw a scatter diagram displaying the data.
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(b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)
Σx =
Σy =
Σx2 =
Σy2 =
Σxy =
r =

(c) Find x, and y. Then find the equation of the least-squares line y hat = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)
x =
y =
y hat =
+
x

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.
WebAssign Plot WebAssign Plot
WebAssign Plot WebAssign Plot

(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 three decimal places. Round your answers for the percentages to one decimal place.)
r2 =
explained
%
unexplained
%

(f) At an archaeological site with elevation 6.0 (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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