data in Appendix 3.13 (data available on Blackboard), which gives predictors for the thrust of a jet engine. The AN OVA table and coefcients table for the regression of thrust on primary speed of rotation (x1), secondary speed of rotation (x2), fuel ow rate (X3), pressure (12;), exhaust temperature (x5), and ambient temperature at the time of the test (x6) are given below. The AN OVA table and coefficients table for the regression of thrust on these six variables are given below. Source SS df Ms F-value p-value Regression 9908846 6 1651474 2350.13 0.000 Error 23190 33 703 Total 9932036 39 Term Coeff SE Coef T-value p-Value VIF Constant -4738 2445 -1.94 0.061 X1 primary 1.119 0.286 3.90 0.000 289.11 X2 secondary -0.0302 0.0382 -0.79 0.435 71.83 X3 fuel 0.231 0.118 1.95 0.059 168.05 X4 pressure 3.85 2.69 1.43 0.161 219.97 X5 exhaust 0.822 0.351 2.34 0.025 32.41 X6 ambtemp -16.95 2.62 -6.47 0.000 8.48 a) (2) From the individual ttests, which variables are significant at u=0.05 (assuming all the other variables in the model) for predicting thrust? b) (6) Consider a reduced model that excludes secondary speed of rotation (x2) and pressure (x4). The ANOVA table for this model is given below. Perform the partial Ftest to determine if at least one of these variables are needed in the model. Give the value of your test statistic, the critical value (or p-value), and your conclusion regarding the necessity of secondary speed of rotation and pressure. Source 38 df Ms F-value p-value Regression 9907039 4 2476760 3467.86 0.000 Error 24997 35 714 Total 9932036 39 "y(thrust) ", "x1 (speedl) ", "x2 (speed2) ", "x3(fuelflow) ", "x4 (pressure) ", "x5 (exhausttemp) ", "x6 ( ambienttemp) " 4540 , 2140 , 20640, 30250, 205, 1732,99 4315, 2016, 20280, 30010, 195, 1697, 100 4095, 1905 , 19860, 29780, 184, 1662,97 3650, 1675, 18980, 29330, 164, 1598,97 3200 , 1474, 18100, 28960, 144, 1541,97 4833, 2239, 20740, 30083, 216, 1709,87 4617, 2120, 20305, 29831, 206, 1669,87 4340 , 1990, 19961, 29604, 196, 1640,87 3820, 1702, 18916, 29088, 171, 1572,85 3368 , 1487, 18012 , 28675, 149, 1522, 85 4445 , 2107, 20520 , 30120, 195, 1740, 101 4188 , 1973, 20130 , 29920, 190, 1711, 100 3981, 1864, 19780, 29720, 180, 1682, 100 3622, 1674, 19020, 29370, 161, 1630, 100 3125 , 1440, 18030 , 28940, 139, 1572, 101 4560, 2165, 20680 , 30160, 208, 1704,98 4340, 2048, 20340, 29960, 199, 1679,96 4115 , 1916, 19860, 29710, 187, 1642,94 3630 , 1658, 18950 , 29250, 164, 1576,94 3210, 1489 , 18700, 28890, 145, 1528,94 4330 , 2062, 20500 , 30190, 193, 1748, 101 4119 , 1929, 20050, 29960, 183, 1713, 100 3891, 1815, 19680, 29770, 173, 1684, 100 3467, 1595, 18890 , 29360, 153, 1624,99 3045 , 1400, 17870, 28960, 134, 1569, 100 4411 , 2047, 20540 , 30160, 193, 1746,99 4203, 1935, 20160 , 29940, 184, 1714,99 3968 , 1807 , 19750, 29760, 173, 1679,99 3531, 1591, 18890, 29350, 153, 1621,99 3074, 1388, 17870, 28910, 133, 1561,99 4350, 2071, 20460 , 30180, 198, 1729, 102 4128, 1944 , 20010 , 29940, 186, 1692, 101 3940, 1831, 19640, 29750, 178, 1667, 101 3480, 1612, 18710, 29360, 156, 1609, 101 3064 , 1410, 17780 , 28900, 136, 1552, 101 4402, 2066, 20520 , 30170, 197, 1758, 100 4180, 1954 , 20150 , 29950, 188, 1729,99 3973, 1835, 19750, 29740, 178, 1690,99 3530, 1616, 18850, 29320, 156, 1616,99 3080, 1407, 17910, 28910, 137, 1569, 100