We wish to optimize the performance of a process with two adjustable parameters. The table below contains measured data of the cost function that we wish to minimize. It is common to fit such data to a polynomial model. A possible optimum can then be calculated based on the model equation (the predicted conditions should later on be verified experimentally). It is important to avoid extrapolating outside of the region of data. a) Visualize the measured data points (F(P1,P2)). Keep in mind that these are discreet points and you have no information what lies between the data. As F is a function of two independent variables ( P1 and P2 ) you will need to create a three-dimensional plot (e.g. plot 3 ) b) The plot created in a) is tricky to interpret, but it appears that there might be a minimum somewhere but there are not enough data points to estimate it from the graph. Try to fit the data with a model suitable to identify a minimum. First, second and third order polynomial models for two independent variables are as follows: Festes,1=a0+a2P1+a2P2 Fest2=a0+a2P1+a2P2+a3P12+a4P22+as3P1P2 Fest,3=a0+a3P1+a2P2+a3P12+a4P22+a5P1P2+a6P3+a7P23+a8P12P2+ a9P1P22 Justify your choice and fit the data with the selected model. Calculate R2. c) Visualize the model by adding a response surface based on the model equation to the previous plot (See example in lecture 7). d) It might be hard to see if the actual data points are captured by the response surface. Instead create a 'parity plot'. Plot the measured F values (from table) vS. computed values (for the same P1 and P2 values) using your model equation. Comment on the plot. e) Find the minimum of the function you have obtained from the regression analysis. Where is the minimum ( P1 and P2 ) and what is the value for F at the minimum