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 |
5.50 |
6.25 |
6.75 |
7.25 |
7.50 |
y |
9 |
38 |
38 |
50 |
72 |
What percentage of the variation in y can be
explained by the corresponding variation in x and
the least-squares line?
Select one:
a. 0.3%
b. 89.9%
c. 1.0%
d. 10.1%
e. 94.8%
The best linear regression line is y = -137.96 + 26.97 * x.
and 89.9% percentage of the variation in y can be explained by the corresponding variation in x.
x <- c(5.50,6.25,6.75,7.25,7.50)
> y <- c(9,38,38,50,72)
> fit <- lm(y~x)
> fit
Coefficients:
(Intercept) x
-137.96 26.97
> summary(fit)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -137.956 34.880 -3.955 0.0288 *
x 26.971 5.215 5.172 0.0140 *
Residual standard error: 8.368 on 3 degrees of freedom
Multiple R-squared: 0.8992, Adjusted
R-squared: 0.8655
F-statistic: 26.75 on 1 and 3 DF, p-value: 0.01403
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