It is thought that prehistoric Indians did not take their best tools, pottery, a
ID: 3250033 • Letter: I
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) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico: x 5.75 6.25 6.75 7.75 8.25 y 31 26 38 74 72 Find the value of the coefficient of determination r2.
a. –0.061
b. 0.883
c. –0.883
d. –0.117
e. –0.939
Explanation / Answer
values are calculated in table as shown below.
Formula for coefficient of determination r2.
r^2 = { ( 1 / N ) * [ (xi - x) * (yi - y) ] / (x * y ) }2
where N is the number of observations used to fit the model, is the summation symbol, xi is the x value for observation i, x is the mean x value, yi is the y value for observation i, y is the mean y value, x is the standard deviation of x, and y is the standard deviation of y.
coefficient of determination r2. = 0.8826 = 0.883
Answer is option B)
X Y XY X^2 Y^2 5.75 31 178.25 33.0625 961 6.25 26 162.5 39.0625 676 6.75 38 256.5 45.5625 1444 7.75 74 573.5 60.0625 5476 8.25 72 594 68.0625 5184Related Questions
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