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 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 .

Answer 1

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