Coir fiber, derived from coconut, is an eco-friendly material with great potential for u...

Coir fiber, derived from coconut, is an eco-friendly material with great potential for use in construction. The article “Seepage Velocity and Piping Resistance of Coir Fiber Mixed Soils” (J. of Irrig. and Drainage Engr., 2008: 485–492) included several multiple regression analyses. The article’s authors kindly provided the accompanying

a. Here is output from fitting the model with the three x_i’s as predictors:

How would you interpret the number –.0003020 in the Coef column on output?

b. Does fiber content appear to provide useful information about velocity provided that fiber length and hydraulic gradient remain in the model? Carry out a test of hypotheses.

c. Fitting the model with just fiber length and hydraulic gradient as predictors gave the estimated regression coefficients when fiber length = 25 and hydraulic gradient = 1.2 . Is there convincing evidence that true average velocity is something other than .1 in this situation? Carry out a test using a significance level of .05.

d. Fitting the complete second-order model (as did the article’s authors) resulted in SSE = .003579 . Does it appear that at least one of the second-order predictors provides useful information over and above what is provided by the three first-order predictors? Test the relevant hypotheses.