Electrical energy. A combined cycle power plant (CCPP) is composed of gas turbines, steam turbines, and heat recovery steam generators. In a CCPP, the electricity is ENRGY generated by gas and steam turbines, which are combined in one cycle, and is transferred from one turbine to another. The vacuum has an effect on the steam turbine. A set of 40 data points was collected from a CCPP, including measurements of the exhaust vacuum (cm Hg) and the net hourly electrical energy output (MW). The data are listed in the accompanying table.

a. Construct a scatterplot for these data.

b. Does it appear that a second-order model might better explain the variation in energy than a first-order model? Explain.

c. Fit a first-order model to these data.

d. Fit a second-order model to these data.

e. Compare the results in parts c and d and decide which model better explains variation in energy. Justify your choice. Multiple regression models can also be written to include qualitative (or categorical) independent variables. Qualitative variables, unlike quantitative variables, cannot be measured on a numerical scale. Therefore, we must code the values of the qualitative variables (called levels) as numbers before we can fit the model. These coded qualitative variables are called dummy (or indicator) variables because the numbers assigned to the various levels are arbitrarily selected. To illustrate, suppose a female executive at a certain company claims that male executives earn higher salaries, on average, than female executives with the same education, experience, and responsibilities. To support her claim, she wants to model the salary y of an executive using a qualitative independent variable representing the gender of an executive (male or female). 12.7 Qualitative (Dummy) Variable Models Data for Exercise 12.65 Vacuum, x Energy, y Vacuum, x Energy, y 40.77 480.48 52.05 464.82 58.49 445.75 64.96 427.28 56.9 438.76 68.31 441.7649.69 453.09 41.04 474.71 40.66 464.4340.71 467.21 39.16 470.96 35.57 487.69 71.29 442.35 62.44 438.6741.76 464 41.39 485.66 69.51 428.77 58.66 452.16 38.18 484.31 67.45 429.87 68.67 435.29 41.23 468.82 46.93 451.41 56.85 442.85 70.04 426.25 36.08 483.26 37.49 480.66 67.45 433.59 44.6 460.17 71.29 433.04 64.15 453.13 52.75 458.6 43.56 461.7170.79 435.14 44.63 471.08 75.6 443.2 40.46 473.74 39.61 477.9 41.1 448.56 60.29 445.26