EG-285: Supplementary Mini Project

Instructions.
The mark awarded for this supplementary mini project will contribute 100% towards your module grade for EG-285. (If this is a 1st sit attempt because of agreed extenuating circumstances, it will contribute 70% and will be combined with the two pieces of coursework set during the semester 1).
Answer all the questions within a Word document that should not exceed 10 pages of size A4 with a minimum font size of 12 (including necessary tables and figures). Submit this
Background.
A control engineeris trying to optimize the conversion rate (Y) during a reaction experiment. The three control variables in this experiment are the reaction time(X1),reaction temperature (X2) and the amount of catalyst (X3).The results of carrying out an experiment where thesecontrol variables are set at different values is shown in the table below. The variables X1 to X3 have been re scaled to fall within the same limits of -1.682 to +1.682, whilst the conversion rate (Y) is shown as a percentage.
Time, X1    Temperature,X2    Catalyst,X3    Conversion (%), Y
-1    -1    -1    75
1    -1    -1    51
-1    1    -1    88
1    1    -1    70
-1    -1    1    71
1    -1    1    90
-1    1    1    66
1    1    1    97
0    0    0    81
0    0    0    75
0    0    0    76
0    0    0    83
-1.682    0    0    76
1.682    0    0    79
0    -1.682    0    85
0    1.682    0    97
0    0    -1.682    55
0    0    1.682    81
0    0    0    80
0    0    0    90

Questions.
1.    Using the above data set and the technique of multiple least squares, estimate the ? parameters of the following second order response surface model:

where Y is the conversion rateand ? is the prediction error or residual. X1 is the time, X2 is the temperatureand X3 is the catalyst.How good a fit is this model to the actual data?
[20%]
2.    Identify which variables are statistically significant at the 5% significance level. State any assumptions that need to be made in assessing such statistical significance, and where appropriate construct suitable plots to validate these assumptions.                                  [35%]

3.    Estimate the parameters of the simplified version of the model shown in question1 above, that includes only the statistically significant variables (at the 5% significance level).Using these estimates for ?, describe in words, the effect of a unit change in temperature.
[20%]

4.    Usingyoursimplified model, what set ofoperating conditions (within the range of the experimental values shown in the table above) would you recommend if it is critical to maximise the conversion rate. Make full use of any suitable 2D or 3D scatter plots to explain these conditions.                                [25%]

EG-285: Supplementary Mini Project
Instructions.
The mark awarded for this supplementary mini project will contribute 100% towards your module grade for EG-285. (If this is a 1st sit attempt because of agreed extenuating circumstances, it will contribute 70% and will be combined with the two pieces of coursework set during the semester 1).
Answer all the questions within a Word document that should not exceed 10 pages of size A4 with a minimum font size of 12 (including necessary tables and figures). Submit this
Background.
A control engineeris trying to optimize the conversion rate (Y) during a reaction experiment. The three control variables in this experiment are the reaction time(X1),reaction temperature (X2) and the amount of catalyst (X3).The results of carrying out an experiment where thesecontrol variables are set at different values is shown in the table below. The variables X1 to X3 have been re scaled to fall within the same limits of -1.682 to +1.682, whilst the conversion rate (Y) is shown as a percentage.
Time, X1    Temperature,X2    Catalyst,X3    Conversion (%), Y
-1    -1    -1    75
1    -1    -1    51
-1    1    -1    88
1    1    -1    70
-1    -1    1    71
1    -1    1    90
-1    1    1    66
1    1    1    97
0    0    0    81
0    0    0    75
0    0    0    76
0    0    0    83
-1.682    0    0    76
1.682    0    0    79
0    -1.682    0    85
0    1.682    0    97
0    0    -1.682    55
0    0    1.682    81
0    0    0    80
0    0    0    90

Questions.
1.    Using the above data set and the technique of multiple least squares, estimate the ? parameters of the following second order response surface model:

where Y is the conversion rateand ? is the prediction error or residual. X1 is the time, X2 is the temperatureand X3 is the catalyst.How good a fit is this model to the actual data?
[20%]
2.    Identify which variables are statistically significant at the 5% significance level. State any assumptions that need to be made in assessing such statistical significance, and where appropriate construct suitable plots to validate these assumptions.                                  [35%]

3.    Estimate the parameters of the simplified version of the model shown in question1 above, that includes only the statistically significant variables (at the 5% significance level).Using these estimates for ?, describe in words, the effect of a unit change in temperature.
[20%]

4.    Usingyoursimplified model, what set ofoperating conditions (within the range of the experimental values shown in the table above) would you recommend if it is critical to maximise the conversion rate. Make full use of any suitable 2D or 3D scatter plots to explain these conditions.                                [25%]

EG-285: Supplementary Mini Project
Instructions.
The mark awarded for this supplementary mini project will contribute 100% towards your module grade for EG-285. (If this is a 1st sit attempt because of agreed extenuating circumstances, it will contribute 70% and will be combined with the two pieces of coursework set during the semester 1).
Answer all the questions within a Word document that should not exceed 10 pages of size A4 with a minimum font size of 12 (including necessary tables and figures). Submit this
Background.
A control engineeris trying to optimize the conversion rate (Y) during a reaction experiment. The three control variables in this experiment are the reaction time(X1),reaction temperature (X2) and the amount of catalyst (X3).The results of carrying out an experiment where thesecontrol variables are set at different values is shown in the table below. The variables X1 to X3 have been re scaled to fall within the same limits of -1.682 to +1.682, whilst the conversion rate (Y) is shown as a percentage.
Time, X1    Temperature,X2    Catalyst,X3    Conversion (%), Y
-1    -1    -1    75
1    -1    -1    51
-1    1    -1    88
1    1    -1    70
-1    -1    1    71
1    -1    1    90
-1    1    1    66
1    1    1    97
0    0    0    81
0    0    0    75
0    0    0    76
0    0    0    83
-1.682    0    0    76
1.682    0    0    79
0    -1.682    0    85
0    1.682    0    97
0    0    -1.682    55
0    0    1.682    81
0    0    0    80
0    0    0    90

Questions.
1.    Using the above data set and the technique of multiple least squares, estimate the ? parameters of the following second order response surface model:

where Y is the conversion rateand ? is the prediction error or residual. X1 is the time, X2 is the temperatureand X3 is the catalyst.How good a fit is this model to the actual data?
[20%]
2.    Identify which variables are statistically significant at the 5% significance level. State any assumptions that need to be made in assessing such statistical significance, and where appropriate construct suitable plots to validate these assumptions.                                  [35%]

3.    Estimate the parameters of the simplified version of the model shown in question1 above, that includes only the statistically significant variables (at the 5% significance level).Using these estimates for ?, describe in words, the effect of a unit change in temperature.
[20%]

4.    Usingyoursimplified model, what set ofoperating conditions (within the range of the experimental values shown in the table above) would you recommend if it is critical to maximise the conversion rate. Make full use of any suitable 2D or 3D scatter plots to explain these conditions.                                [25%]