The objective of the experiment was to maximize the illumination of flares in candles. The four ingredients used were magnesium (x1), sodium nitrate (x2), strontium nitrate (x3) and a binder (x4). The response was the number of candles that illuminated. Assuming that the amount of binder was kept constant, the experimental design with response is given below x1 x2 x3 Y 0.4 0.1 0.47 75 0.4 0.1 0.42 180 0.6 0.1 0.27 195 0.6 0.1 0.22 300 0.4 0.47 0.1 145 0.4 0.42 0.1 230 0.6 0.27 0.1 220 0.6 0.22 0.1 350 0.5 0.1 0.345 220 0.5 0.345 0.1 260 0.4 0.2725 0.2725 190 0.6 0.1725 0.1725 310 0.5 0.235 0.235 260 0.5 0.21 0.21 410 0.5 0.2225 0.2225 425
a. Create a preliminary analysis and draw conclusions
b. Give a distribution for the errors (Justify your answer)
c. Is there an overdispersion in this case? (Justify your answer)
d. Determine the best model for this situation (Model must fit well and be adequate)
e. Make a recommendation to the experimenter that meets the objective