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.

Data set:

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

What is the estimated regression model?

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.

What is the ratio of the largest standard deviation to the smallest standard deviation (in one decimal place)?

What is the estimated standard error of the model (2 decimal places)?

Answer 1

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

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Factor	3	4134.0	1378.00	42.84	0.000
Error	20	643.3	32.17
Total	23	4777.3

The hypothesis being tested is:

H0: β1 = β2 = β3 = β4 = 0

H1: At least one βi ≠ 0

The p-value is 0.000.

Since the p-value (0.000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the model is significant.

The ratio of the largest standard deviation to the smallest standard deviation = 1.8

The estimated standard error of the model = 5.67