Question

In: Statistics and Probability

To detect the presence of harmful insects in farm fields, we can put up boards covered...

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

Solutions

Expert Solution

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:

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

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