Cardanol, an agricultural by-product of cashew nut shells, is a cheap and abundantly available renewable resource. In Industrial & Engineering Chemistry Research (May 2013), researchers investigated the use of cardanol as an additive for natural rubber. Cardanol was grafted onto pieces of natural rubber latex and the chemical properties examined. One property of interest is the grafting efficiency (measured as a percentage) of the chemical process. The researchers manipulated several independent variables in the chemical process: x1 = initiator concentration (parts per hundred resin), x2 = cardanol concentration (parts per hundred resin), x3 = reaction temperature (degrees Celsius), and x4 = reaction time (hours). Values of these variables, as well as the dependent variable y = grafting efficiency, were recorded for a sample of n = 9 chemical runs. The data are provided in the accompanying table. A MINITAB analysis of the first-order model, E(y1) = β0 + β1x1 + β2x2 + β3x3 + β4x4, is also shown.
a. Conduct a test of overall model adequacy. Use a = .10.
b. Interpret practically the value of R2α.

c. Interpret practically the value of s.
d. Find and interpret a 90% confidence interval for b3.
e. Conduct a test of H0: β4 = 0. What do you conclude?

Transcribed Image Text:

CC x2) RTEMP (x3) Run GE (V) IC (x1) RTIME (X) 81.94 52.38 1. 54.62 84.92 78.93 36.47 67.79 43.96 42.85 --2226n en en Regression Analysis: GE versus lIC, CC, RTEMP, RTIME The regression equation is GE - 97.3 - 5.72 IC - 3.36 CC + 0.433 RIEMP - 1.69 RIIME Predictor Coef SE Coef Constant 97.28 27.40 3.55 0.024 IC -5.723 4.581 -1.25 0.280 -3.3570 0.9162 -3.66 0.022 RTEMP 0.4330 0.3054 1.42 0.229 RTIME -1.685 2.290 -0.74 0.503 S - 11.2206 R-Sa - 81.4 R-Sq (adj) - 62.9% Analysis of Variance Source DF MS 4 2208.2 552.1 4.38 0.091 4 503.6 125.9 Regreasion Residual Error Total 8 2711.8