Question
Question: 12.69 The Longhaul Transport Company wishes to predict the price of petrol based on international crude oil prices. They record average monthly petrol prices
Question: 12.69 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.
Answer only part 2 question.
Part 2 Comment on whether you think the errors in Ex 12.69 are autocorrelated, supporting your answer with a sequential residual plot and a Durbin-Watson statistic calculation.
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