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 ybe 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: x6.006.507.258.009.00y116351765 Find a for the equation of the least-squares line . Round your answer to three decimal places.

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Asked Jul 16, 2019
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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 ybe 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

7.25

8.00

9.00

y

1

16

35

17

65

 

Find a for the equation of the least-squares line . Round your answer to three decimal places.

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Expert Answer

Step 1

Given data obtained for a collection of archeological sites in New Mexico as shown below. 

The least square regression line is in the form of y = α + β x, where β is the slope and α is the y intercept. Both can be calculated using the below mentioned formulae

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6 6.5 7.25 9 Χ 1 16 35 17 65 Υ ΝΣyy-ΣΝΣy β= ΝΣ ()- (Σ ) Σy-ΒΣΧ α- Ν

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Step 2

Using the data finding all the values needed to compute the least square line as shown below we get

&...

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x^2 Χ Χ: 6 1 6 36 6.5 16 104 253.75 42.25 7.25 35 52.5625 17 136 64 585 Σx=36.75|Σy= 134|ΣΣν 1084.75| Σx^2-275.8125 65 81

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