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

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Regression C1 Petrol Temp C2 Tank Temp C3 Initial Pressure 4 Petrol Pressure C5 Hydrocarbons Responses: Hydrocarbons Continuous predictors: Petrol Temp Tank Temp 'Initial Pressure Petrol Pressure Categorical predictors: Model Coding... Options... Stepwise 」 Select Graphs··· Results. sprage. .. Help OK Cancel

MINITAB OUTPUT:
MTB > Regress;
SUBC> Response 'Hydrocarbons';
SUBC> Nodefault;
SUBC> Continuous 'Petrol Temp' 'Tank Temp' 'Initial Pressure' 'Petrol Pressure';
SUBC> Terms C1 C2 C3 C4;
SUBC> Constant;
SUBC> Unstandardized;
SUBC> Tmethod;
SUBC> Tanova;
SUBC> Tsummary;
SUBC> Tcoefficients;
SUBC> Tequation;
SUBC> TDiagnostics 0.

Regression Analysis: Hydrocarbons versus Petrol Temp, Tank Temp, Initial Pres, Petrol Press
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 4 2507.38 626.844 79.04 0.000
Petrol Temp 1 0.64 0.641 0.08 0.778
Tank Temp 1 85.57 85.567 10.79 0.003
Initial Pressure 1 12.35 12.349 1.56 0.223
Petrol Pressure 1 68.53 68.525 8.64 0.007
Error 27 214.12 7.931
Total 31 2721.50

RULE: If p-value is less than alpha (alpha=0.05) , then we Reject H0 and conclude that the variable is Significant.

Here, Tank Temp (p-val=0.003) and Petrol Pressure (p-val=0.007) are significant components (variables) of the model.

Model Summary
S R-sq R-sq(adj) R-sq(pred)
2.81612 92.13% 90.97% 88.26%

Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 7.28 3.16 2.30 0.029
Petrol Temp -0.048 0.169 -0.28 0.778 13.02
Tank Temp 0.404 0.123 3.28 0.003 4.48
Initial Pressure -0.534 0.428 -1.25 0.223 70.50
Petrol Pressure 1.186 0.404 2.94 0.007 58.78

Regression Equation Hydrocarbons = 7.28 - 0.048 Petrol Temp + 0.404 Tank Temp - 0.534 Initial Pressure + 1.186 Petrol Pressure

Fits and Diagnostics for Unusual Observations
Obs Hydrocarbons Fit Resid Std Resid
18 46.00 44.82 1.18 0.60 X
23 31.00 36.49 -5.49 -2.27 R
26 37.00 31.24 5.76 2.15 R
R Large residual
X Unusual X

Prediction:

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Predict Response: Hydrocarbons Enter individual values Petrol Temp Tank Temp Initial Pressure Petrol Pressur 28 30 45 40 Results ! Eentedel.. Select storage … Help Cancel OK

MTB > Predict 'Hydrocarbons';
SUBC> Nodefault;
SUBC> KPredictors 28 30 45 40;
SUBC> TEquation;
SUBC> TPrediction.

Prediction for Hydrocarbons
Regression Equation
Hydrocarbons = 7.28 - 0.048 Petrol Temp + 0.404 Tank Temp - 0.534 Initial Pressure
+ 1.186 Petrol Pressure

Variable Setting
Petrol Temp 28
Tank Temp 30
Initial Pressure 45
Petrol Pressure 40

Fit SE Fit 95% CI 95% PI
41.4836 2.39709 (36.5652, 46.4020) (33.8955, 49.0716) X

X denotes an unusual point relative to predictor levels used to fit the model.

Predicted amount of hydrocarbons is-

MTB > Let k1 = 7.28-0.048*28+0.404*30-0.534*45+1.186*40
MTB > print k1
Data Display
K1 41.4660

On comparing we observe that, we can be about 95 % confident in this prediction.