STAT 600 - Assignment #7 MANOVA

Include your JMP results for all problems.

Problem 1 – Plastic Film

The optimum conditions for extruding plastic film have been examined using a technique called Evolutionary Operation. In the course study that was done, three responses - Y1=tear resistance, Y2=gloss, and Y3=opacity – were measured at two levels of the factors, X1=rate of extrusion and X2=amount of additive. The measurements were repeated n=5 times at each combination of the factor levels. The data are contained in the file Plastic Film.JMP.

a)  Conduct appropriate analyses to compare the mean of each response separately across for the two rate of extrusion levels. You can do this by selecting Fit Y by X and putting all three responses in the Y box and rate of extrusion in the X box. If you hold down the Ctrl key while selecting the analysis options for tear resistance (Y1), it will do the same for the other two responses as well. Briefly summarize your findings. (6 pts.)

b)  Repeat part (a) but this time, consider the potential effect of the amount of additive. Does amount of additive seems to have any effect on these plastic film properties? (6 pts.)

c)  Use Rows > Color or Marker by Column to color code the points by amount of additive. The use Fit Y by X to plot gloss (Y) vs. tear (X) and then select Group By… from the Bivariate Fit pull-down menu and finally select Density Ellipse > .90 from the same pull-down menu. Explain how the resulting plot shown below, created using the procedure above, that the amount of additive actually might impact both tear resistance and gloss. (3 pts.)

d)  Conduct a two-way MANOVA to determine if rate of extrusion and/or amount of additive effect the responses. Summarize your findings. (6 pts.)

Problem 2 – Fatty Acid Concentrations of Italian Olive Oils

This is an open ended problem, think of it like a mini-midterm (a week or so late). Researchers are interested in characterizing differences in the fatty acid content of olive oils made from olives grown in different regions of Italy. There are two geographic classifications in these data. The first classification is nine individual growing areas in Italy (Area Name) – East Liguria, West Liguria, Umbria, North-Apulia, South-Apulia, Sicily, Coastal Sardinia, Inland-Sardinia, and Calabria. A broader classification is the growing region in Italy (Region Name) – Northern, Southern, and Sardinia. The map below should help in your understanding of where these areas/regions are located in Italy.

The fatty acids measured are as follows:

Palmitic C16H32O2

Palmitoleic C16H30O2

Stearic C18H36O2

Oleic C18H34O2

Linoleic C18H32O2

Eicosanoic C20H40O2

Linolenic C18H30O2

Molecular formulae taken from Wikipedia, so if these are wrong it is not my fault. I don’t understand how small differences in the number of carbon and hydrogen molecules make distinct fatty acids. Chemistry is weird!

Research Question/Problem:

Use any/all descriptive and inferential methods you think are appropriate to characterize the differences in the amino acid content between the olive oils produced in each growing region/area in Italy. Summarize your findings for the researchers. Be sure to include all relevant plots and analysis summaries in your report. (100 pts.)