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 xbe 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 |
5.50 |
6.50 |
7.50 |
7.75 |
8.75 |
y |
15 |
32 |
55 |
39 |
72 |
Find aand b for the equation of the least-squares
line .
The statistical software output for this problem is:
Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = -75.923077 + 16.461538 x
Sample size: 5
R (correlation coefficient) = 0.93717051
R-sq = 0.87828857
Estimate of error standard deviation: 8.7917502
Parameter estimates:
Parameter | Estimate | Std. Err. | Alternative | DF | T-Stat | P-value |
---|---|---|---|---|---|---|
Intercept | -75.923077 | 25.775189 | ? 0 | 3 | -2.9455876 | 0.0602 |
Slope | 16.461538 | 3.5379921 | ? 0 | 3 | 4.6527912 | 0.0187 |
Analysis of variance table for regression
model:
Source | DF | SS | MS | F-stat | P-value |
---|---|---|---|---|---|
Model | 1 | 1673.3154 | 1673.3154 | 21.648466 | 0.0187 |
Error | 3 | 231.88462 | 77.294872 | ||
Total | 4 | 1905.2 |
Hence,
a = -75.923
b = 16.462
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