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	6.00	6.50	7.00	8.00	8.50
y	50	46	61	96	90

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Find a for the equation of the least-squares line .

Group of answer choices

–81.093

1433.442

–1433.442

–218.293

1419.042

Answer 1

solution,

X	Y	XY	X^2	Y^2
6	50	300	36	2500
6.5	46	299	42.25	2116
7	61	427	49	3721
8	96	768	64	9216
8.5	90	765	72.25	8100

n	5
sum(XY)	2559.00
sum(X)	36.00
sum(Y)	343.00
sum(X^2)	263.50
sum(Y^2)	25653.00
Numerator	447.00
Denominator	477.75
r	0.9356
r square	0.8754
Xbar(mean)	7.2000
Ybar(mean)	68.6000
b	20.7907
a	-81.0930

b = 20.7907

a = -81.0930

= a + bx

= - 81.0930 + 20.7907x