Table 1. Raw data for a random sample of 15 vehicles from the EPA Automative 'Ii'ends Database. Model Year MPG Weight Displacement Class 2015 21.54716 4124.129 178.5575 Truck 2007 17.02911 4736.041 236.0139 Truck 2003 19.33 781 3777.898 179.4107 Truck 1986 23.02399 3174.024 190.2972 Car 2017 22.54566 4650.112 164.4554 Truck Prelim. 2021 32.38923 3194.868 114.4701 Car 2000 22.51440 3400.909 168.2990 Car 2014 22.18444 4453.683 208.4433 Truck 1999 21.50476 3879.585 197.3525 Car 2012 27.21958 3450.740 137.7964 Car 1990 23.73371 2929.358 122.0215 Car 1998 24.57349 3304.248 142.4937 Car 2007 19.09633 4461.215 218.8619 Truck 2002 15.44052 4987.675 302.1571 Truck 1988 16.42429 4357.654 239.6896 Truck 2. Answer the following based on a multiple linear regression, predicting mpg with weight (1:1) and engine displacement (mg). (a) Fit the specied model. Write the model equation, including your estimates. (b) Test the null hypothesis that the slope of 2:1, ,81, is equal to zero. State the hypotheses, test statistic, rejection region(s), and p-value. Interpret the conclusion of this test at o: = 0.05. (c) Consider at; = 3000 and at; = 150. Calculate a 95% condence interval for E[Y|ml = mi, 532 = 23;]. Calculate a 95% prediction interval for y\" given .121 = 3:; and .122 = 33;. Interpret both of these intervals in context. ((1) Which model constitutes the \"complete\" model and which the \"reduced\" model? Can 1:2 be dropped from the model without losing predictive information? Test at the o: = 0.05 signicance level