Question

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

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 6.75 7.25 7.50 8.00 y 47 71 48 71 89 ​ Find the equation of the least squares line . Round a and b to three decimal places.

Homework Answers

Answer #1

Solution :

X Y XY X^2 Y^2
5.75 47 270.25 33.0625 2209
6.75 71 479.25 45.5625 5041
7.25 48 348 52.5625 2304
7.5 71 532.5 56.25 5041
8 89 712 64 7921
n 5
sum(XY) 2342.00
sum(X) 35.25
sum(Y) 326.00
sum(X^2) 251.44
sum(Y^2) 22516.00
Numerator 218.50
Denominator 303.64
r 0.7196
r square 0.5178
Xbar(mean) 7.0500
Ybar(mean) 65.2000
SD(X) 0.7649
SD(Y) 15.8795
b 14.9402
a -40.1282

Y = a +bx = -40.128 + 14.940x

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