In industry cooling applications (e.g., cooling of nuclear reactors), a process called subcooled flow boiling is often employed. Subcooled flow boiling is susceptible to small bubbles that occur near the heated surface. The characteristics of these bubbles were investigated in Heat Transfer Engineering (Vol. 34., 2013). A series of experiments was conducted to measure two important bubble behaviors- bubble diameter (millimeters) and bubble density (liters per meters squared). The mass flux (kilograms per meters squared per second) and heat flux (megawatts per meters squared) were varied for each experiment. The dataobtained at a set pressure are listed in the following table.

a. Consider the multiple regression model, E(y1) = β0 + β1x1 + β2x2, where y1 = bubble diameter, x1 = mass flux, and x2 = heat flux. Use statistical software to fit the model to the data and test the overall adequacy of the model.
b. Consider the multiple regression model, E(y2) = β0 + β1x1 + β2x2, where y2 = bubble density, x1 = mass flux, and x2 = heat flux. Use statistical software to fit the model to the data and test the overall adequacy of the model.
c. Which of the two dependent variables, diameter (y1) or density (y2), is better predicted by mass flux (x1) and heat flux (x2)?

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Density Bubble Mass Flux Heat Flux Diameter 0.15 1. 406 406 406 406 0.64 1.02 1.15 1.26 13103 29117 123021 165969 0.29 0.37 0.62 4 406 406 811 811 811 811 811 811 1217 1217 1217 0.86 1.00 0.15 0.29 0.37 0.91 0.68 0.58 0.98 1.02 1.17 0.86 0.59 0.49 0.80 0.93 1.06 0.81 0.43 254777 347953 7279 22566 106278 0.62 0.86 1.00 0.15 0.29 0.37 10 11 12 13 14 15 16 17 18 145587 224204 321019 5096 18926 90992 1217 1217 1217 0.62 0.86 1.00 112102 192903 232211