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32 Cooling method for gas turbines. Refer to the Journal of Engineering for Gas Turbines and Power (January 2005) study of a high-pressure inlet...

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4.32 Cooling method for gas turbines. Refer to the Journal of Engineering for Gas Turbines and Power (January 2005) study of a high-pressure inlet fogging method for a gas turbine engine, Exercise 4.13 (p.188). Recall that you fit a first-order model for heat rate (y) as a function of speed x ( ¿¿ 1 ) ¿ , inlet temperature x ( ¿¿ 2 ) ¿ , exhaust temperature x ( ¿¿ 3 ) ¿ , cycle pressure ratio x ( ¿¿ 4 ) ¿ , and air flow rate x ( ¿¿ 5 ) ¿ , to data saved in the GASTURBINE file. a. Researchers hypothesize that the linear relationship between heat rate (y) and temperature (both inlet and exhaust) depends on air flow rate. Write a model for heat rate that incorporates the researchers’ theories. b. Use statistical software to fit the interaction model, part a, to the data in the GASTURBINE file. Give the least squares prediction equation. c. Conduct a test (at α=.05) to determine whether inlet temperature and air flow rate interact to effect heat rate. d. Conduct a test (at α=.05) to determine whether exhaust temperature and air flow rate interact to effect heat rate. e. Practically interpret the results of the tests, parts c and d. 4.36 Cars with catalytic converters. A quadratic model was applied to motor vehicle toxic emissions data collected over 15 recent ears in Mexico City (Environment Science and Engineering, September 1, 2000). The following equation was used to predict the percentage (y) of motor vehicles without catalytic converters in the Mexico City fleet for a given year ( x ) : y = 325,790 321.67 x + 0.794 x 2 . a. Explain why the value β 0 = 325,790 has no practical interpretation.
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b. Explain why the value β 1 = 321.67 should not be interpreted as a slope. c. Examine the value of β 2 to determine the nature of the curvature (upward or downward) in the sample data. d. The researchers used the model to estimate “that just after the year 2021 the fleet of cars with catalytic converters will completely disappear.” Comment on the danger of using the model to predict y in the year 2021. 4.40 Failure times of silicon wafer microchips. Researchers at National Semiconductor experimented with tin-lead solder bumps used to manufacture silicon wafer integrated circuit chips (International Wafer Level Packaging Conference, November 3-4, 2005). The failure times of the microchips (in hours) were determined at different solder temperatures (degrees Centigrade). The data for one experiment are given in the next table (p.208). The researchers want to predict failure time (y) based on solder temperature (x). a) Construct a scatterplot for the data. What type of relationship, linear or curvilinear, appears to exist between failuretime and solder temperature? 10000 8000 6000 4000 2000 0 170 160 150 140 130 120 110 FAILTIME TEMP Scatterplot of TEMP vs FAILTIME b) Fit the model ( y )= β 0 + β 1 x + β 2 x 2 , to the data. Give the least squares prediction equation.
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Statistics II Week 3 Homework_8755653.docx

4.40 Failure times of silicon wafer microchips. Researchers at National Semiconductor
experimented with tin-lead solder bumps used to manufacture silicon wafer integrated circuit
chips...

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