Question: Carbon dioxide flooding experiment. One of the most promising methods for extracting crude oil employs a car­bon dioxide (CO₂) flooding technique. CO₂, when flooded into oil pockets, enhances oil recovery by displacing the crude oil. In a microscopic investigation of the CO₂ flood­ing process, flow tubes were dipped into sample oil pockets containing a known amount of oil (Journal of Petroleum Technology, Aug. 1982). The oil pockets were flooded with CO₂ and the percentage of oil displaced was recorded. The experiment was conducted at three different flow pressures and three different dipping angles. The displace­ment test data are recorded in the accompanying table.

Pressure x1, pounds per square inch	Dipping Angle x2, degrees	Oil Recovery y, percentage
1,000	0	60.58
1,000	15	72.72
1,000	30	79.99
1,500	0	66.83
1,500	15	80.78
1,500	30	89.78
2,000	0	69.18
2,000	15	80.31
2,000	30	91.99

_a. Write the complete second-order model relating percent­age oil recovery y to pressure x₁ and dipping angle x₂.

b. Plot the sample data on a scattergram, with percentage oil recovery y on the vertical axis and pressure x₁ on the horizontal axis. Connect the points corresponding to the same value of dipping angle x₂. Based on the scattergram, do you believe a complete second-order model is appropriate?

c. Fit the interaction model to the data. Give the least-squares predic­tion equation.

d. Construct a plot similar to the scattergram of part b, but use the predicted values from the interaction model on the vertical axis. Compare the two plots. Do you believe the interaction model will provide an adequate fit?

e. Check model adequacy using a statistical test with a = .05.

Is there evidence of interaction between pressure x₁ and dipping angle x₂? Test using a = .05.