To determine characteristics associated with Y = whether a cancer patient achieved remission (1 = yes), a study used logistic regression. 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 π ̂ = 0.068 when LI = 8. B. Show that π ̂ = 0.50 when LI = 26.0 D. The lower quartile and upper quartile for LI are 14 and 28. Show that π ̂ 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
To determine characteristics associated with Y = whether a cancer patient achieved remission (1 = yes), a study used logistic regression. 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 π ̂ = 0.068 when LI = 8. B. Show that π ̂ = 0.50 when LI = 26.0 D. The lower quartile and upper quartile for LI are 14 and 28. Show that π ̂ 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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
100%
To determine characteristics associated with Y = whether a cancer patient achieved remission (1 = yes), a study used logistic regression. 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 π ̂ = 0.068 when LI = 8.
B. Show that π ̂ = 0.50 when LI = 26.0
D. The lower quartile and upper quartile for LI are 14 and 28. Show that π ̂ 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
Transcribed Image Text:Table 4.8. Data for Exercise 4.1 on Cancer Remission
Number of Number of
Number of Number of
Cases Remissions
Cases
LI
8
2
18
1
10
2
20
3
12
3
22
2
14
3
24
1
16
3
26
1
Source: Reprinted with permission from E. T. Lee, Computer Prog. Biomed., 4: 80-92, 1974.
Table 4.9. Computer Output for Problem 4.1
Standard
Error
li
Parameter Estimate
Intercept -3.7771
0.1449
Obs
72
1
Remissions LI
2
li
8
10
0
0
0
0
0
Source
li
1.3786
0.0593
DF
1
remiss
0
0
1
2
1
0
1
n
2
2
LI
28
32
34
38
LR Statistic
Chi-Square
8.30
Number of Number of
Cases Remissions
1
1
1
3
Likelihood Ratio
95% Conf. Limits
pi_hat
0.06797
0.08879
-6.9946 -1.4097
0.0425 0.2846
Pr > ChiSq
0.0040
lower
0.01121
0.01809
1
0
1
2
Chi-Square
7.51
5.96
upper
0.31925
0.34010
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 31 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman