The pharmaceutical industry has increasingly developed “nanoformulations” for drug delivery, but quality control at such a small scale is tricky. The article “Quality by Design Approach Using Multiple Linear and Logistic Regression Modeling Enables Microemulsion Scale Up” (Molecules 2019) describes one study to determine how x = oil concentration (g/100 mL) affects whether a development run meets a certain critical quality attribute (CQA) with respect to polydispersity. Here, y = 1 if the CQA was achieved and = 0 if not.

Software reports coefficients β̂₀ = 11.13 and β̂₁ = −2.68 with estimated standard errors 5.96 and 1.42, respectively.

a. Write out the estimated logit function, and use it to estimate p(2), p(4), and p(6).
b. Does the data provide convincing statistical evidence that oil concentration affects the chance of meeting this particular CQA? Test at the .05 significance level.

c. Construct a 95% CI for β₁, then use this to give an interval estimate for e^β₁. Interpret the latter interval.
d. What does e^β₀ represent in this context? Does that interpretation seem appropriate here? Why or why not?

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