The preliminar analysis shows no problems except a possible nonlinear relationship between Time and Dose
Regression of Time on Dose, Sex and BP Quan shows a bad model, so we will fit a nonlinear model in Dose:
Step 2: Transformations don't work
Step 3: Polynomial Model:
| Model | p-value of highest order term |
| Quadratic | 0.011 |
| Cubic | 0.920 |
Done? But:
Plot of Residuals vs. Fits, identifying observations by Blood Pressure:
Run the regression command with predictors Dose, Dose2, Sex and BP Quan, store Residuals and Fits. Draw the scatterplot of Residuals vs. Fits, with Groups and Regression, Categorial Variable BP Quan
any pattern in the residual vs. fits plot is bad, something is not right here. But what? Remember, we are using the discrete predictors alone, so we are fitting parallel lines. This appears to be a bad idea here.
Let's include some product terms, Dose*Sex and Dose*BP Quan
Regression of Time on Dose, Dose2, Sex, Dose*Sex, BP Quan and Dose*BP Quan:
R2 = 93.7%
Plot of Residuals vs. Fits:
So, what is the best model? Using best subset regression we find that the best model is
Time = 43.4 - 6.98 Dose+ 0.511 Dose^2 + 43.7 BP Quan - 7.53 Dose*BP Quan+ 0.955 Dose*Sex
with a Mallow's Cp=5.0 (Note: no sex)
This means:
Female, low blood pressure: Time = 54.3 - 8.9 Dose + 0.51 Dose^2, minimum is at 8.7 or 10
Female, normal blood pressure: Time = 65.2 - 10.7 Dose + 0.51 Dose^2, minimum is at 10.5 or 10
Female, high blood pressure: Time = 76.2 - 12.5 Dose + 0.51 Dose^2, minimum is at 12.3 or 10
Male, low blood pressure: Time = 54.3 - 7.9 Dose + 0.51 Dose^2, minimum is at 7.7 or 7
Male, normal blood pressure: Time = 65.2 - 9.7 Dose + 0.51 Dose^2, minimum is at 9.5 or 10
Male, high blood pressure: Time = 76.2 - 11.5 Dose + 0.51 Dose^2, minimum is at 11.3 or 10
So for a man with low blood pressure, prescribe 7 gram, for all others 10 gram. Or of course offer a greater variety of pills, one for each case.
How can we interpret these interaction terms?
