A study used logistic regression to determine characteristics associated with Y = whether a cancer patient achieved remission (1 = yes). The most important explanatory variable was a labeling index (LI) that measures proliferative activity of cells after a patient receives an injection of tritiated thymidine.

It represents the percentage of cells that are “labeled.” Table 4.8 shows the grouped data. Software reports Table 4.9 for a logistic regression model using LI to predict π = P(Y = 1).

a. Show how software obtained ˆπ = 0.068 when LI = 8.

b. Show that ˆπ = 0.50 when LI = 26.0.

c. Show that the rate of change in ˆπ isn0.009 when LI = 8 and is 0.036 when LI = 26.

d. The lower quartile and upper quartile for LI are 14 and 28. Show that ˆπ

increases by 0.42, from 0.15 to 0.57, between those values.

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