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 1 shows the grouped data. Software reports Table 2 for a logistic regression model using LI to predict π = P(Y = 1). Show how software obtained = 0.068 when LI = 8. Show that = 0.50 when LI = 26.0. Show that the rate of change in is 0.009 when LI = 8 and is 0.036 when LI = 26. The lower quartile and upper quartile for LI are 14 and 28. Show that increases by 0.42, from 0.15 to 0.57, between those values. When LI increases by 1, show the estimated odds of remission multiply by 1.16. Using information from Table 2, conduct a Wald test for the LI effect. Interpret. Using information from Table 2, construct a Wald confidence interval for the odds ratio corresponding to a 1-unit increase in LI. Interpret. Using information from Table 2, conduct a likelihood-ratio test for the LI effect. Interpret. Using information from Table 2, construct the likelihood-ratio confidence interval for the odds ratio. Interpret.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 1 shows the grouped data. Software reports Table 2 for a logistic regression model using LI to predict π = P(Y = 1).

Show how software obtained = 0.068 when LI = 8.
Show that = 0.50 when LI = 26.0.
Show that the rate of change in is 0.009 when LI = 8 and is 0.036 when LI = 26.
The lower quartile and upper quartile for LI are 14 and 28. Show that increases by 0.42, from 0.15 to 0.57, between those values.
When LI increases by 1, show the estimated odds of remission multiply by 1.16.
Using information from Table 2, conduct a Wald test for the LI effect. Interpret.
Using information from Table 2, construct a Wald confidence interval for the odds ratio corresponding to a 1-unit increase in LI. Interpret.
Using information from Table 2, conduct a likelihood-ratio test for the LI effect. Interpret.
Using information from Table 2, construct the likelihood-ratio confidence interval for the odds ratio. Interpret.