Refer to Exercise 10.14 (p. 578). The researchers concluded that "in order to break a water-oil mixture with ' the lowest possible voltage, the volume fraction of the disperse phase x, should be high, while the salinity x2 and the amount of surfactant x5 should be low." Use this information and the first order model of Exercise 10.14 to find a 95% prediction interval for this "low" voltage y. Interpret the interval.
Exercise 10.14
In the oil industry, water that mixes with crude oil during production and transportation must be
removed. Chemists have found that the oil can be extracted from the water /oil mix electrically. Researchers at the University of Bergen (Norway) conducted a series of experiments to study the factors that influence the voltage (y) required to separate the water from the oil (Journal of Colloid and Interface Science, Aug. 1995). The seven independent variables investigated in the study are listed in the table above. (Each variable was measured at two levels-a "low" level and a "high" level.) Sixteen water/oil mixtures were prepared using different combinations of the independent variables; then each emulsion was exposed to a high electric field. In addition, three mixtures were tested when all independent variables were set to 0. The data for all 19 experiments are also given in the table.
a. Propose a first-order model for y as a function of all seven independent variables.
b. Use a statistical software package to fit the model to the data in the table.
c. Fully interpret the ß estimates.