6. (20 points) Sam is studying the relationship between the weight of a car (annotated as X, and measured in kg) and the fuel consumption (annotated as Y and measured in "miles per gallon" or MPG). She collected data from 9 cars, and the data are listed below: Car 2 w 4 5 6 7 8 9 X 1041 1182 1285 1483 1621 1733 1703 1950 3346 Y 32 28 22 19 18 16.5 13 17.5 10 (a) Assuming that X and Y has a simple linear relationship, or Y=A+BX. Please estimate the regression coefficients A and B. For A and B, please save your results to 5 decimal places. (b) Predict the MPG of a car whose weight is 1800 kg. Save your result to 2 decimal places (c) At 5 % significance level, please test the hypothesis that the weight of a car does not affect MPG. In another word, please test that B = 0 You may use the online t-distribution calculator to solve the question (note the v= degrees of freedom in the calculator, you can specify P to obtain x, or specify x to obtain the relevant P): https://homepage.divms.uiowa.edu/~mbognar/applets/t.html