1. A motorist found that the efficiency of her engine could be increased by adding lubricating oil to fuel. She experimented with different amounts of lubricating oil and the data are Amount of lubricating oil (ml) |0 25 50 75 100 Efficiency (%) 60 70 75 81 84 (a) (10 points) Obtain the least squares fit of a straight line to the amount of lubricating oil. (b) (10 points) Test whether or not the slope B, = 0. Take o = 0.05 as your level of significance. (c) (10 points) Construct a 90% confidence interval on the mean response at To = 10 ml. (d) (10 points) Give a point estimate of the mean engine efficiency when the amount of lubricating oil is 450 ml. (e) (10 points) What additional danger is there when using your estimate in part (d)