Question

An ecologist’s study found a relationship between the density of acorns produced in the fall and the density of deer tick larvae the following spring could be approximated by the linear equation y = x + 5 where x is the number of acorns per square meter in the fall and y is the number of deer tick larvae per 10 square meters in the following spring. You decide to test this model by collecting data for several years: Year 1 Year 2 Year 3 Acorns/m2 (x) 30 22 34 Deer tick larvae/10m2 (y) 30 25 40

	year 1	year 2	year 3
acorns/ m^2 (x)	30	22	34
deer tick larvae /10m^2 (y)	30	25	40

(a) How many deer tick larvae per 10 square meters did the study predict you would observe in the spring of Year 2 (after observing 22 acorns the previous fall)?

(b) Calculate the sum of squares error between your data and the linear equation proposed by the study.

Answer 1

(a) y = 23.92857143

(b) The sum of squares error = 16.0714

	r²	0.862
	r	0.929
	Std. Error	4.009
	n	3
	k	1
	Dep. Var.	y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	100.5952	1	100.5952	6.26	.2421
Residual	16.0714	1	16.0714
Total	116.6667	2
Regression output				confidence interval
variables	coefficients	std. error	t (df=1)	p-value	95% lower	95% upper
Intercept	-1.6071
x	1.1607	0.4639	2.502	.2421	-4.7342	7.0557