A client from the Department of Mechanical Engineering approached the Consulting Center at Virginia Polytechnic Institute and State University for help in analyzing an experiment dealing with gas turbine engines. Voltage output of engines was measured at various combinations of blade speed and voltage measuring sensor extension. The data are as follows:

(a) Fit a multiple linear regression to the data,

(b) Compute (-tests on coefficients. Give P-values.

(c) Comment on the quality of the finedmodel.

Speed, (volts) (in./sec) 6336 Extension, 2 (in.) 0.000 0.000 0.000 0.000 0.000 0.000 0.006 0.006 0.006 0.006 0.012 0.012 0.012 1.95 2.50 2.93 1.69 1.23 3.13 1.55 1.94 2.18 2.70 1.32 7099 8026 6230 5369 8343 6522 7310 7974 8501 6646 7384 1.60 1.89 s000 Speed, E1 (in./sec) Extension, (volts) (in.) 0.012 0.018 0.018 2.15 1.09 1.26 8545 6755 7362 7934 1.57 1.92 0.018 0.018 8554