Question

6. A study used logistic regression to determine characteristics associated wi th Y wheth er a cancer patient achieved remission (I yes). The most important explanatory variabl was a labeling index (LI) receives an injection of tritiated thymidine. It represents the percentage o "labeled". Results from fitting a logistic regression model using LI to predict π-p 1) are given below: that measures proliferative activity of cells after a patient (Y = Standard Error Constant -3.7771 1.3786 0.1449 0.0593 Parameter Estimate LI Obs LI remiss pi_hat lower upper 0.06797 0.01121 0.31925 0.08879 0.01809 0.34010 2 10 a. Show how the software calculated π 0.068 when LI 8 b. Find the value of LI such that 0.5 c. When LI increases by 1, show that the estimated odds of remission multiply by 1.16.

Answer 1

This is logistic Regression.

1+ єー(-3.777 1+0.1449* LI)

a. Putting, LI = 8 in the above equation we get $\hat \pi$ = 0.068

b. Rewriting the above equation,

log-3.77710.1449 LI

Putting, $\hat \pi$ = 0.5, we get, LI = 26.07

c. Let us assume the odd ratio = R,

where, $R = \frac{\hat \pi}{1 - \hat \pi}$

so, log(R) = -3.7771 + 0.1449 * LI

Partially differentiating both sides we get,

dR/R = 0.1449 * d(LI)

Given, d(LI) = 1,

So, dR = 0.1449 * R

So the answer should be 0.1449. But given 1.16. I think the question is wrong. You check with your professor. If he/she still says that the question is correct you comment, I will update the answer.