Question 4: More than one response variables. (30 points) The coded factor settings and results from an experiment are shown below. The objective is to look for the settings to achieve a high yield and low filtration time Yield Field Crystal Filtration Trial X1 (gs) Color Growth Time 21.1 Blue None 150 N - 0 23.7 Blue None 10 3 + 20.7 Red None 8 4 0 - 21.1 Slightly red None 35 Blue Very O 0 24.1 8 slight 6 O + 22.2 Unobserved Slight 7 7 + 18.4 Slightly red Slight 18 8 + 0 23.4 Red Much 8 9 + + 21.9 Very red Much 10 Variable Level Variable + x, = Condensation temperature (C) 90 100 110 x, = Amount of B (cm') 24.4 29.3 34.2 (a) Analyze the data to obtain your best model: i. Describe your approach and steps of analysis. ii. Report your model expression, the overall goodness-of-fit (e.g. ANOVA, esp. Rsquare and Adjusted Rsquare), estimated parameters, and their significance results (t-ratio or p-value). Hint: fit a second-order polynomial model by stepwise least square regression with each of the two responses. Take the logarithm of filtration time to fit a better model. (b) Based on your model, draw contour diagrams for yield and filtration time. (c) Find the settings of x, and x within the range enclosed by the experiment design levels that give i . The highest predicted yield, and ii. The lowest predicted filtration time. Hint: optimize each response separately. If you use an analytical method, you should check whether the true maximum/minimum condition is satisfied. (d) Specify the optimal set of conditions for a, and x, that will simultaneously give high yield and low filtration time. At this set of conditions what field color and how much crystal growth would you most likely expect? Hint: Give a best approximation of the optimal condition, either graphically or using a more formal analytical approach