Researchers are investigating whether patients with moderate cases of COVID-19 can be helped by a certain antiviral drug. Arriving patients are classified according to the presence (1) or absence (0)...

Researchers are investigating whether patients with moderate cases of COVID-19 can be helped by a certain antiviral drug. Arriving patients are classified according to the presence (1) or absence (0) of four different risk factors (D = diabetes, H = heart disease, IS = immune suppressed, A = over 65). Within each risk combination, the patients are randomly assigned to a drug (AV = 0 for placebo or 1 for antiviral). The data is available on the text Web site as datatab_11_risks. Only 11 of the 16 possible risk combinations (or 22 of the 32 drug/risk combinations) are present in the data. Some risk combinations were much more common than others. The dependent variable is the number of days till hospital discharge (HOSP_TIME).

(a) Construct a cell mean plot where the 11 risk factor combinations are on the horizontal axis.

(b) Conduct a one-way ANOVA to see if any of the 22 groups differ significantly with respect to mean HOSP_DAYS.

(c) Fit a linear model using AV and the risk factors H, D, IS, and AGE, together with the interactions of AV with each risk factor. How do you interpret the regression results? How do they compare to the impressions from the cell mean plot?

(d) Conduct a lack of fit test for the model in part (b) versus that in part (c).