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]