The following table results from a study on the treatment of arthritis pain. Male and female subjects received an active or placebo treatment for their arthritis pain, and the subsequent extent of improvement was recorded as marked, some, or none. In the following analysis, take male and placebo as reference groups.

Sex Treatment Improvement

Female Active 50 15 20

Female Placebo 18 21 56

Male Active 15 7 21

Male Placebo 3 2 30 2

-Ignoring the ordering information in the response to treatment, and taking "no improvement" as the reference group, fit the saturated polytomous logistic regression model that contains interaction between treatment and gender. Write down your fitted regression equation(s).

-Ignoring the ordering information in the response to treatment, and taking "no improvement" as the reference group, fit a polytomous logistic regression model with main effects for treatment and sex. Write down your fitted regression equation(s).