The Longhaul Transport Company wishes to predict the price of petrol based on international crude oil prices. They record average monthly petrol prices and crude oil prices over a 12-month period.

Month	Petrol price / litre)	Crude oil price (/barrel)
January	1.25	72
February	1.32	75
March	1.15	69
April	1.35	82
May	1.22	78
June	1.26	80
July	1.43	91
August	1.29	84
September	1.28	82
October	1.17	79
November	1.52	98
December	1.43	91

a. Plot a scatter diagram and, assuming a linear relationship, use the least-squares method to calculate the regression coefficients, b0 and b1.

b. Interpret the meaning of the Y intercept, b0, and the slope, b1, in this problem. c. Use the prediction line developed in (a) to predict the petrol price if crude oil is $75/barrel. d. Calculate the coefficient of determination, r2, and interpret its meaning in this problem. e. Perform a residual analysis and determine the adequacy of the fit of the model. f. At the 0.05 level of significance, is there evidence of a significant linear relationship between petrol and crude oil prices? g. Construct a 95% confidence interval estimate for the mean petrol price if crude oil is $75/barrel. h. Construct a 95% prediction interval for a particular petrol price if crude oil is $75/barrel. i. Construct a 95% confidence interval estimate of the population slope.