In a simulation of 30 mobile computer networks, the average speed, pause time, and number of neighbors were measured. A “neighbor” is a computer within the transmission range of another. The data are presented in the following table.

Neighbors Speed Pause Neighbors Speed Pause Neighbors Speed Pause 10.17 5 0 9.36 5 10 8.92 5 20 8.46 5 30 8.30 5 40 8.00 5 50 10.20 10 0 8.86 10 10 8.28 10 20 7.93 10 30 7.73 10 40 7.56 10 50 10.17 20 0 8.24 20 10 7.78 20 20 7.44 20 30 7.30 20 40 7.21 20 50 10.19 30 0 7.91 30 10 7.45 30 20 7.30 30 30 7.14 30 40 7.08 30 50 10.18 40 0 7.72 40 10 7.32 40 20 7.19 40 30 7.05 40 40 6.99 40 50

a. Fit the model with Neighbors as the dependent variable, and independent variables Speed, Pause, Speed ⋅ Pause, Speed2, and Pause2.

b. Construct a reduced model by dropping any variables whose P-values are large, and test the plausibility of the model with an F test.

c. Plot the residuals versus the fitted values for the reduced model. Are there any indications that the model is inappropriate? If so, what are they?

d. Someone suggests that a model containing Pause and Pause2 as the only dependent variables is adequate. Do you agree? Why or why not?

e. Using a best subsets software package, find the two models with the highest R2 value for each model size from one to five variables. Compute Cp and adjusted R2 for each model.

f. Which model is selected by minimum Cp? By adjusted R2? Are they the same?