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 data on x1 = fiber content s% d, x2 = fiber length (mm), x3 = hydraulic gradient (no unit provided), and y = seepage velocity (cm/sec).

a. Here is output from fitting the model with the three xi'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 β^0 = - .005315, β^1 = .0004968, and β^2 = .102204 (the t ratios for these two predictors are both highly significant). In addition, sY^ = .00286 when fiber length 5 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.

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758 99 7 4 78 00 22 4 60 i 5 8 2 3 4 60 70 8 1 4 4 4 3 5 2 2 4 2 9 8 0 5 9 8 3 5 6 9 6 6 3 5 6 3293 00 98 26 27 09 72 80 74 56 29 98 99 7 8 2 90 39 % 4 5 4 2 4 74 81 83 62 05 87 54 79 86 57 9 05 79 26 70 44 36 50 89 22 77 26 83 h0 0 0 0 0 0 0 0 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 0 0 0 0 40 40 60 60 60 60 60 60 60 In .0 0 0 0 0 0 0 0 5 5 5 5 5 5 0 0 0 0 0 0 0 0 0 5 5 5 5 5 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 26 27 28 29 30 3 3 3 3 3 3 3 3 39 40 4 4 4 44 5 6 7 8 9 1 2 3 4 6 7 9 0 1 2 3 4 6 7 19 Predictor Constant fib cont fib lngth 0.0003020 0.0001676-1.80 0.078 hyd grad 0.102489 0.004711 21.76 0.000 Coef SE Coef -0.002997 0.007639 -0.39 0.697 -0.012125 0.007454-1.63 0.111 S= 0.0162355 R-Sq = 91.6% R-Sq (adj )=91.1% souro Regression Reaidual Error 45 0.011862 0.000264 Total MS 3 0.129898 0.043299 164.27 0.000 48 0.141760