A study8 investigated characteristics associated with y = whether a cancer patient achieved remission (1 = yes, 0 = no). An important explanatory variable was a labeling index (LI = percentage of “labeled” cells) that measures proliferative activity of cells after a patient receives an injection of tritiated thymidine. Table 4.5 shows the data and R output for a logistic regression model.

a. Show that Pˆ(Y = 1) = 0.50 when LI = 26.0.

b. When LI increases by 1, show that the estimated odds of remission multiply by 1.16.

c. Summarize the LI effect by how Pˆ(Y = 1) changes over the range or interquartile range of LI values.

d. Show that the rate of change in Pˆ(Y = 1) is 0.009 when LI = 8.

e. Summarize the LI effect by the estimated average marginal effect.