Question

2. When petrol is pumped into tanks, hydrocarbons escape. To evaluate the effectiveness of pollution controls, experiments were performed. The quantity of hydrocarbons escaping was measured as a function of the tank temperature, the temperature of the petrol pumped in the initial pressure in the tank, and the pressure of the petrol pumped i a) The data is in the same data file as the previous question. Copy it into Minitab and run a regression analysis for the quantity of hydrocarbons as a function of the other variables. This would take the form h Ao + β1x1 +AgT2 + β3x3 + β42:4-1 mark for output (b) From hypothesis tests on al the Bs, decide which ones are significant components of the model. Write the final regression equation. 8 marks (c) Predict the quantity of hydrocarbons released for the following values of the predictors (in order): (30, 28, 45, 40). How confident can you be in this prediction? 3 marks 1 Teap X) VP(Y) Petrol TeTank TenInitial TPetrol Pr Hydrocarbons gn.) 0.7 12 24 5.1 21 4. 3 10. 4 14. 7 17.4 21 25. 5 28. 7 24 35. 6 39. 5 15 13 67 49. 7 16 15 16 16 31 31 16 16 15 30 30 16 16 17 17 30 24 18 16 20 16 15 28 24 18 17 16 28 16 27 15 15 19 18 19 19 16

Answer 1

Here are the answers to the questions asked:

(a) Hydrocarons as a function of other variables

1 7277379 191-4.8 12 12 1841 * 10-2A +4.043 101567 * 10-32-5.337763393 * 10-1A+ 1.1861058984

(b) For The t-value is -6.57238. The p-value is < .00001

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For $\beta _{2}$ The t-value is -7.82738. The p-value is < .00001

For $\beta _{3}$ The t-value is 0.3303. The p-value is .371193.

For $\beta _{4}$ The t-value is -0.55318. The p-value is .291064

So from the above analysis the significant components are Petrol Temperature and Tank Temperature

7.277379191-4.812121841 * 10-2A 4.043 10 1567 * 10-32 h

(c) Based on the above equation the predicted value of the quantity of hydrocarbons for (30,28,45,40) is 17.1544270263