Linear Regression Question R3 The table below presents data from the 1975 volume of Motor Trend concerning the gasoline mibage performance and the engine displacement for 15 automobiles. Fit a regression model relating mileage performance and engine displacement. How significant is the relationship? EEDIZEEL'EEEIIE 18.9 El 1. Use a scatterplot in order to explain the relationship between X and Y a. What do you expect for the sign of [31 and magnitude of rz? Note that the magnitude of r2 depends on the strength of the linear relationship between X and Y. 2. After running the regression model in Minitab: a. What is the estimated regression equation? b. interpret the estimate of Ba in the words of the problem. Do the same for Bi. c. Conduct a test that the true slope of the model differs from 0. Explain how to use the output of the regression for the test. d. Relate the conclusion of your test to the scatterplot that you generated in (1) e. Use the generated plots of the regression model (histogram of the residuals) in order to check the normality assumption of your model. While there is no need for a statistical test, you must compare the shape to a normal distribution pdf. 3. Generate the fitted line plot for this regression 4. Generate prediction interval for 57 and confidence interval for E(y) when xp = f. (if is the average of given x's)