An experiment to evaluate the effects of certain variables on soil erosion was p

Question

An experiment to evaluate the effects of certain variables on soil erosion was performed on 10-foot-square plots of sloped farmland subjected to 2 inches of artificial rain applied over a 20-minute period. The data and related ANOVA table are as follows:

a. Compute R2, and comment on the fit of the model. b. The fitted model involving all three independent variables is given by = -1.879 + 77.326X1 + 1.559X2 - 23.904X3. Compute and compare observed and predicted values of Y for plots 1, 5, and 7.

Plot SL (Y) SGOT) LOBS 10 27.1 35.6 31.4 37.8 40.2 39.8 55.5 43.6 52.1 43.8 35.7 0.13 0.47 0.44 0.48 0.48 0.49 0,53 0,50 0.55 0.51 0.48 1.95 5.13 3.98 6.25 7.12 6.500 10,67 7.08 9,88 8.72 496 0.26 0.16 0.18 0.29 0.25 0.10 0.19 0.32

Explanation / Answer

a) R2 = 680.4912/696.5855 = 0.9768 = 97.68% of the variability in y variable can be "explained by" variation in the other variables

b) The predicted equation is = -1.879 + 77.326X1 + 1.559X2 - 23.904X3

For Plot 1, x1 = 0.43, x2 = 1.95, x3 = 0.34

The predicted value at those points is = -1.879 + 77.326(0.43) + 1.559(1.95) - 23.904(0.34)

=26.2838

The actual value of the Y is 27.1

Error = actual value - predicted value = 27.1-26.2838 = 0.81613

For Plot 5

x1 = 0.48, x2 = 7.12, x3 = 0.25

The predicted value at those points is = -1.879 + 77.326(0.48) + 1.559(7.12) - 23.904(0.25)

=

The actual value of the Y is 40.2

Error = actual value - predicted value = 40.36156 -40.2 = -0.16156

For Plot 7

x1 = 0.53, x2 = 10.67, x3 =0.10

The predicted value at those points is = -1.879 + 77.326(0.53) + 1.559(10.67) - 23.904(0.10)

=53.348

The actual value of the Y is 55.5

Error = actual value - predicted value = 55.5 - 53.348 = 2.15209

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