Question

Smitley and Davis studied the changes in gypsy moth egg mass density over one generation as a function of the initial egg mass density in a control plot and two treated plots. The data below are for the control plot.

Initial Egg Mass (per 0.04 ha)	50	75	100	160	175	180	200
Change in Egg Mass Density (%)	250	-100	-25	-25	-50	50	0

A. On the basis of the data given in the table, find the best-fitting logarithmic function using least squares. State the square of the correlation coefficient. (Note that the authors used logarithms to the base 10.) (Use 4 decimal places in your answers.)
y(x) =

r² =

B. Use this model to estimate the change in egg mass density with an initial egg mass of 120 per 0.04 ha. (Use 4 decimal places in your answer.)
With an initial egg mass of 120 per 0.04ha, the change in mass density is

%

Answer 1

Smitley and Davis studied the changes in gypsy moth egg mass density over one generation as a function of the initial egg mass density in a control plot and two treated plots. The data below are for the control plot.

Initial Egg Mass (per 0.04 ha)	50	75	100	160	175	180	200
Change in Egg Mass Density (%)	250	-100	-25	-25	-50	50	0

A. On the basis of the data given in the table, find the best-fitting logarithmic function using least squares. State the square of the correlation coefficient. (Note that the authors used logarithms to the base 10.) (Use 4 decimal places in your answers.)

y(x) =513.2945-239.6202 *log10(x)

r² =0.2340

B. Use this model to estimate the change in egg mass density with an initial egg mass of 120 per 0.04 ha. (Use 4 decimal places in your answer.)
With an initial egg mass of 120 per 0.04ha, the change in mass density is

15.0807%

Regression Analysis
	r²	0.2340	n	7
	r	-0.4837	k	1
	Std. Error	108.838	Dep. Var.	Change in Egg Mass Density (%)
ANOVA table
Source	SS	df	MS	F	p-value
Regression	18,092.4716	1	18,092.4716	1.53	.2714
Residual	59,228.9570	5	11,845.7914
Total	77,321.4286	6
Regression output					confidence interval
variables	coefficients	std. error	t (df=5)	p-value	95% lower	95% upper
Intercept	513.2945	405.8668	1.265	.2617	-530.0195	1,556.6085
Log10(Initial Egg Mass (per 0.04 ha))	-239.6202	193.8905	-1.236	.2714	-738.0316	258.7912

when x=120,

y(120) =513.2945-239.6202 *log10(120) =15.080674