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). (solved)Show how software obtained = 0.068 when LI = 8. (solved)Show that = 0.50 when LI = 26.0. (solved)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.
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). (solved)Show how software obtained = 0.068 when LI = 8. (solved)Show that = 0.50 when LI = 26.0. (solved)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.
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
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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).
- (solved)Show how software obtained = 0.068 when LI = 8.
- (solved)Show that = 0.50 when LI = 26.0.
- (solved)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.
Transcribed Image Text:Parameter Estimate
Intercept
-3.7771
0.1449
li
Table 2. Computer Output
Obs
1
2
li
8
10
Source
li
Standard
Error
remiss
0
0
1.3786
0.0593
DF
1
n
LR Statistic
Chi-Square
8.30
22
2
Likelihood Ratio
95% Conf. Limits
2
-6.9946 -1.4097
0.0425
0.2846
pi_hat
0.06797
0.08879
Pr > ChiSq
0.0040
lower
0.01121
0.01809
Chi-Square
7.51
5.96
upper
0.31925
0.34010
Transcribed Image Text:Number of Number of
LI Cases Remissions
82246
10
12
14
16
2333N
0
0
0
0
0
LI
18
20
22
24
26
Number of Number of
Cases
Remissions
1
3
2
1
1
1
2
1
0
1
LI
28
32
34
38
Number of Number of
Cases
Remissions
1
1
1
3
1
0
1
2
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