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 multiple regression.

Conduct the global test of model significance. Use a type 1 error rate of 5%. Write all the steps of the hypothesis testing process. Clearly define what the regression parameters mean.

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 hypothesis being tested is:

H₀: β₁ = β₂ = β₃ = 0

H₁: At least one β_i ≠ 0

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the model is significant.

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