The following table contains some information about the model used. Assume the probabilities given by the model are those of being a good writer.
Variable
estimate
CI for exp(b)
constant
-16.71
Sex
0.46
(0.17,2.32)
level 1
0.88
(0.46,12.68)
level 2
0.16
(0.25,5.58)
Score
0.80
(1.40,3.53)
Suppose the 63 students come from a random sample of students in BC and a principal in a school wants to use this study to get information about good writers. The principal has a lot of questions regarding the probability of being a good writer for different values combinations of the explanatory variables. The questions below are some of those questions posed by the principal.
1. She wants to know the probability of being a good writer for a girl in 5th grade with a score of 18 and for a boy in 7th grade with a score of 12.
2. For boys in 5th grade, she wants to know what is the minimum score needed in order to have a probability greater than 0.5 of being a good writer? What is the minimum score needed in order to have a probability greater than 0.5 of being a good writer for girls on 4th grade?
3. How can you interpret the 95% CI for exp(b1) where b1 is the coefficient corresponding to the sex variable and what can you tell to the principal in terms of differences between girls and boys?
4. The principal tells you that she doesn't really understand about odds and odds ratios and requests that you give her instead a 95% CI for b_{1}. Obtain this interval and mention what can you tell to the principal in terms of differences between girls and boys according to it.