Question

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 = 5.22 5.69 6.25 6.75 7.25 y 17 12 33 37 62What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? a. 95.7% b. 0.7% c. 8.4% d. 91.6% e. 4.3%

Answer 1

(B) 0.7%

Explanation:

X = Land Elevation (in ,000 feet)

Y = Unidentified Artifacts (in %)

The hypothetical theory says that:

The higher the elevation, the higher the percentage of unidentified artifacts in the location.

To find the percentage of variation in Y that can be explained by variations in X, we find the slope of the graph of X on Y.

Transforming X to thousand feets, we have 5220, 5690, 6250, 6750, 7250. This is in the attachment, plotted against 17, 12, 33, 37 and 62 respectively.

Further calculations, along with the graph, are in the attachment below. The answer therein is (B) 0.7%