Question

To detect the presence of harmful insects in farm fields, we can put up boards covered with a sticky material and examine the insects trapped on the boards. Which colors attract insects best? Experimenters placed six boards of each of four colors at random locations in a field of oats and measured the number of cereal leaf beetles trapped. The data is in the file Beetles.xlsx under the Quiz4 Resource folder. Analyze the data using a multiple linear regression model.

What is the estimated regression model? Use the original variables and report your results in 2 decimal places.

Blue	Green	White	Red
16	37	21	45
11	32	12	59
20	20	14	48
21	29	17	46
14	37	13	38
7	32	20	47

Answer 1

The estimated regression model is:

Predicted(Number of Beatles Trapped) = 16.17 - 1.33 Blue + 15 Green + 31 Red

Beetles trapped	Blue	Green	Red
16	1	0	0
11	1	0	0
20	1	0	0
21	1	0	0
14	1	0	0
7	1	0	0
37	0	1	0
32	0	1	0
20	0	1	0
29	0	1	0
37	0	1	0
32	0	1	0
45	0	0	1
59	0	0	1
48	0	0	1
46	0	0	1
38	0	0	1
47	0	0	1
21	0	0	0
12	0	0	0
14	0	0	0
17	0	0	0
13	0	0	0
20	0	0	0

The output is:

	R²	0.865
	Adjusted R²	0.845
	R	0.930
	Std. Error	5.672
	n	24
	k	3
	Dep. Var.	Beetles trapped
ANOVA table
Source	SS	df	MS	F	p-value
Regression	4,134.0000	3	1,378.0000	42.84	6.80E-09
Residual	643.3333	20	32.1667
Total	4,777.3333	23
Regression output				confidence interval
variables	coefficients	std. error	t (df=20)	p-value	95% lower	95% upper
Intercept	16.17
Blue	-1.33	3.2745	-0.407	.6882	-8.1638	5.4971
Green	15.00	3.2745	4.581	.0002	8.1696	21.8304
Red	31.00	3.2745	9.467	7.88E-09	24.1696	37.8304