Refer to the Applied Spectroscopy study of the optical density (y) for infrared absorption of the liquid

Question:

Refer to the Applied Spectroscopy study of the optical density (y) for infrared absorption of the liquid PPFPO, Exercise 11.63. In addition to optical density, band frequency (x₁) and film thickness (x₂) were measured for 12 experiments. (The data are saved in the PPFPO file.)
a. Write an interaction model for optical density (y) as a function of band frequency (x₁) and film thickness (x₂).

b. Give a practical explanation of the statement, “band frequency (x₁) and film thickness (x₂) interact.”

c. A MINITAB printout for the interaction model, part a, is shown at the bottom of the page. Give the least squares prediction equation.

d. Is there sufficient evidence (at α = .01) of interaction between band frequency and film thickness?

e. For each level of film thickness (x₂), use the β estimates of the model to sketch the relationship between optical density (y) band frequency (x₁).

Data from Exercise 11.63

Poly (perfluoropropyleneoxide), i.e., PPFPO, is a viscous liquid used extensively in the electronics industry as a lubricant. In a study reported in Applied Spectroscopy (Jan. 1986), the infrared reflectance spectra properties of PPFPO were examined. The optical density (y) for the prominent infrared absorption of PPFPO was recorded for different experimental settings of band frequency (x1) and film thickness (x2) in a Perkin– Elmer Model 621 infrared spectrometer. The results are given in the table below.