An article in Analytical Biochemistry [Application of Central Composite Design for DNA Hybridization Onto Magnetic Microparticles, (2009, Vol. 391(1), 2009, pp. 1723)] considered the effects

An article in Analytical Biochemistry [€œApplication of Central Composite Design for DNA Hybridization Onto Magnetic Microparticles,€ (2009, Vol. 391(1), 2009, pp. 17€“23)] considered the effects of probe and target concentration and particle number in immobilization and hybridization on a micro particle-based DNA hybridization assay. Mean fluorescence is the response. Particle concentration was transformed to surface area measurements. Other concentrations were measured in micromoles per liter (μM). Data are in Table E14-2.

(a) What type of design is used?

(b) Fit a second-order response surface model to the data.

(c) Does a residual analysis indicate any problems?

Hybridization (cm?) Probe area (M) Immobilization Target () Mean area (cm?) Fluorescence Run 0.35 1 0.35 0.025 0.025 4.7 0.35 0.025 0.025 4.7 2.5 0.35 28.0 0.35 0.025 4 2.5 0.35 0.025 81.2 0.025 0.35 0.025 3.5 5.7 3.5 0.025 0.025 6. 3.8 3.5 0.025 12.2 0.35 2.5 2.5 0.025 8. 3.5 19.5 0.35 9. 0.025 0.35 5 4.4 0.35 2.6 10 0.025 5 0.35 83.7 11 2.5 0.35 5 84.7 12 2.5 0.35 5 0.35 3.5 13 0.025 5 6.8 3.5 14 0.025 5 2.4 2.5 0.35 15 5 76 3.5 16 2.5 3.5 5 77.9 17 0.35 5 2 2.5 42.6 18 2 2.5 52.3 0.025 19 3.5 2 2.5 2.6 20 3.5 2.5 2 2.5 72.8 21 3.5 5 0.35 2.5 47.7 22 3.5 5 2.5 54.4 3.5 30.8 23 3.5 5 2 0.025 24 3.5 5 2 5 64.8 25 3.5 5 2.5 51.6 2.5 26 3.5 2 52.6 27 3.5 5 2 2.5 56.1