The PLANTS2 data file gives data on four different species of plants grown in a
ID: 3202629 • Letter: T
Question
The PLANTS2 data file gives data on four different species of plants grown in a laboratory. The species are Leucaena leucocephala, Acacia saligna, Prosopis juliflora, and Eucalyptus citriodora. The researchers who collected these data were interested in commercially growing these plants in parts of the country of Jordan where there is very little rainfall. To examine the effect of water, they varied the amount per day from 50 millimeters (mm) to 650 mm in 100 mm increments. There were four plants per species-by-water combination. There are two response variables. They are fresh biomass and dry biomass. High values for both of these variables are desirable.
Examine the residuals for the two response variables. Are there any unusual patterns or outliers? If you think that there are one or more points that are somewhat extreme, rerun the two-way analysis without these observations. Does this change the results in any substantial way?
Explanation / Answer
Result:
Examine the residuals for the two response variables. Are there any unusual patterns or outliers? If you think that there are one or more points that are somewhat extreme, rerun the two-way analysis without these observations. Does this change the results in any substantial way?
MINITAB used
General Linear Model: fbiomass versus species, water
Method
Factor coding (-1, 0, +1)
Factor Information
Factor Type Levels Values
species Fixed 4 1, 2, 3, 4
water Fixed 7 1, 2, 3, 4, 5, 6, 7
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
species 3 458295 152765 81.45 0.000
water 6 491948 81991 43.71 0.000
species*water 18 60334 3352 1.79 0.040
Error 84 157551 1876
Total 111 1168129
Model Summary
S R-sq R-sq(adj) R-sq(pred)
43.3083 86.51% 82.18% 76.02%
Fits and Diagnostics for Unusual Observations
Obs fbiomass Fit Resid Std Resid
44 184.8 266.0 -81.2 -2.17 R
50 422.9 343.3 79.7 2.12 R
52 199.5 343.3 -143.8 -3.83 R
53 555.3 397.4 157.9 4.21 R
55 311.1 397.4 -86.3 -2.30 R
R Large residual
The main effects species and water, interaction effects all are significant.
Observations 52 and 53 are large residuals.
After removing 52 and 53,
General Linear Model: fbiomass versus species, water
Method
Factor coding (-1, 0, +1)
Factor Information
Factor Type Levels Values
species Fixed 4 1, 2, 3, 4
water Fixed 7 1, 2, 3, 4, 5, 6, 7
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
species 3 437130 145710 123.54 0.000
water 6 478487 79748 67.61 0.000
species*water 18 51868 2882 2.44 0.003
Error 82 96717 1179
Total 109 1028234
Model Summary
S R-sq R-sq(adj) R-sq(pred)
34.3435 90.59% 87.50% 83.13%
After removing the extreme values results are not changed.
General Linear Model: dbiomass versus species, water
Method
Factor coding (-1, 0, +1)
Factor Information
Factor Type Levels Values
species Fixed 4 1, 2, 3, 4
water Fixed 7 1, 2, 3, 4, 5, 6, 7
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
species 3 50524 16841.3 79.93 0.000
water 6 56624 9437.3 44.79 0.000
species*water 18 8419 467.7 2.22 0.008
Error 84 17698 210.7
Total 111 133265
Model Summary
S R-sq R-sq(adj) R-sq(pred)
14.5153 86.72% 82.45% 76.39%
Coefficients
Fits and Diagnostics for Unusual Observations
Obs dbiomass Fit Resid Std Resid
44 59.14 95.10 -35.96 -2.86 R
48 79.80 106.81 -27.01 -2.15 R
52 65.17 103.18 -38.01 -3.02 R
53 172.65 119.62 53.03 4.22 R
111 78.85 53.60 25.25 2.01 R
R Large residual
The main effects species and water, interaction effects all are significant.
Observations 52 and 53 are large residuals.
After removing 52 and 53,
General Linear Model: dbiomass versus species, water
Method
Factor coding (-1, 0, +1)
Factor Information
Factor Type Levels Values
species Fixed 4 1, 2, 3, 4
water Fixed 7 1, 2, 3, 4, 5, 6, 7
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
species 3 48947 16315.5 111.27 0.000
water 6 54798 9133.1 62.29 0.000
species*water 18 7383 410.1 2.80 0.001
Error 82 12023 146.6
Total 109 121859
Model Summary
S R-sq R-sq(adj) R-sq(pred)
12.1088 90.13% 86.88% 82.41%
After removing the extreme values results are not changed.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.