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. Consider the first-order model

E(y) = β_o + β₁x₁ + β₂x₂

a. Construct Y and X matrices for the data.

b. Find X'X and X'Y.

c. Use the technique outlined in Appendix A.4 to find (X'X)^-1. (Be sure to carry out your calculations to six significant digits.)

d. Find the β̂ matrix and the least-squares prediction equation.

e. Find s and interpret its value.

f. Find R_a² and interpret its value.

g. Conduct a test of overall model adequacy using α = .10.

h. Find and interpret a 90% confidence interval for β₁.

i. Find and interpret a 90% confidence interval for β₂.

j. Find and interpret a 90% prediction interval for y when x₁ = 950 and x₂ = .62.    

Transcribed Image Text:

PPFPO Band Frequency X1, cm-1 Film Thickness Optical Density y X2, milligrams .231 740 1.1 .107 740 .62 .053 740 31 .129 805 1.1 .069 805 .62 .030 805 .31 1.005 980 1.1 .559 980 .62 321 980 31 2.948 1,235 1.1 1.633 1,235 62 .934 1,235 31