The Journal of Space Engineering (Vol. 4, 2011) investigated the properties of large, deployable space membranes used to store structures such as solar sails, antennas, sunshields, and solar power satellites. These membranes are susceptible to creases during folding and packaging, which can have a detrimental effect on deployment. The study examined the relationship between the size of the mesh (in millimeters) around the crease and the contact force (Newtons per millimeter) exerted on the membrane. Data for n = 4 experiments on folded space membranes are provided in the table.

a. Fit the straight-line model, to the data, E(y) = β_{0} + β_{1}x, where y = contact force and x = mesh size.

b. Obtain influence diagnostics for the model, part a. Identify any influential observations.

c. Examine a scatterplot of the data. Locate the influential observation on the graph. What does this point suggest about the relationship between y and x?

d. Now fit the quadratic model, E(y) = β_{0} + β_{1}x + β_{2}x^{2} to the data. Comment on the fit of this model as compared to the straight-line model.