1. [19 marks] Fuel economy improvement continues to be a focus in all aspects of engine design and operation. Researchers investigated the effect of lubricant properties on the Fuel Economy Increment in Coordinating European Council standard engine fuel economy tests. Download the le FEI . csv, which contains the following variables: (a) FEI Fuel economy increment. EtaJITHS High shear viscosity (in 3'1) measured at 150C. Use Python to construct a linear regression model predicting the Fuel Economy Increment from the oil's high shear viscosity and give the summary output. Produce diagnostic plots for the linear regression t. Give these plots captions and gure numbers and refer to them as needed in later questions. [3 marks] Give the residual for the observation with a fuel economy increment of 2.6 and a high shear viscosity of 3 3'1. [1 mark] List the assumptions of the linear regression model. For each, explain whether or not there is evidence that this assumption is violated, based on the diagnostic plots. [8 marks] FOR THE REMAINING QUESTIONS ASSUME THE MODEL ASSUMPTIONS ARE SATISFIED. Provide a brief interpretation of the estimated slope and intercept of the model. [2 marks] Report a 99% condence interval for the slope of the linear regression model. [2 marks] Provide a both a 90% prediction interval for the fuel economy increment for an oil with a high shear viscosity of 3.1 3'1 and a 90% condence interval for the expected fuel economy increment for an oil with a high shear viscosity of 3.1 3'1. Briey explain the difference of between the two intervals. [2 marks] Explain the meaning of the Rsquared value in the regression output. [1 mark] \fFirebed Cooling FT TSP Off 785.8724891 17.08145207 Off 786.8501239 12.97628334 Off 764.4880366 11.62975799 Off 764.5982251 14.99460429 Off 779.7449961 16.56468048 Off 776.1461558 17.13700392 Off 739.5256283 15.60135337 Off 804.8289263 17.81024242 Off 738.7401368 14.58445165 Off 767.7566082 6.727850378 Off 760.0315258 18.22799455 Off 812.7143412 13.43555397 Off 758.450688 12.55518423 Off 773.9842117 14.73733535 Off 688.6824091 16.0241901 Off 766.5182957 13.3373858 Off 818.9413956 14.8076318 Off 711.3332471 15.74761897 Off 752.9665672 17.88310595 Off 747.1324152 19.28045463 Off 725.9272784 19.24758319 Off 734.403879 15.29316816 Off 806.1269581 17.22857745 Off 716.6671471 16.5122621422 On On On On On On On On On On On On On On On On On On On On On On 743.0515944 759.5582501 732.7710981 71 7.4325462 746.0136497 709.5324419 779.90121 79 797.6865148 750.970707 754.2140166 744.7494018 770.9164709 738.8106189 746.4720277 775.8057022 764.1 912182 727.923597 744.6652638 795.9234455 747.6626439 774.5290416 729.4702301 751 .120347 814.484767 772.6271101 15.80470615 15.21 46812 1365826414 15.32964557 13.1 7935644 13.1 5459316 14.60638907 12.49747818 10.1 6481492 12.8379871 12.2 54741 63 13.50927603 13.82193162 10.77635601 13.06490733 1 1 .66403407 15.32366866 14.26320016 13.66125801 1 1 .1 9460133 1 1 .72375902 13.77550769 13.41 313375 1 1 .86499443 8.523996799 On On On On On On On On On On On On On On On On On 738.8106189 746.4720277 775.8057022 764.1 912182 727.923597 744.6652638 795.9234455 747.6626439 774.5290416 729.4702301 751 .120347 814.484767 772.6271 101 777.2047974 785.6629968 733.5780437 781 .6800843 13.82193162 10.77635601 13.06490733 11 .66403407 15.32366866 14.26320016 13.66125801 1 1 .1 9460133 11 .72375902 13.77550769 13.41 313375 11 .86499443 8.523996799 14.08306573 13.38576732 11 .1 5575209 12.71 151973