Question 2. In a medical experiment, two different treatment methods are randomly assigned to diabetes patients. The results are as follows. The numbers in the table refer to the number of cases.
\begin{tabular}{|l|l|lll|}
\hline Treatment & Sex & Worsened & No change & Improved \\
\hline A & Male & 155 & 215 & 280 \\
& Female & 75 & 180 & 95 \\
\hline B & Male & 85 & 95 & 75 \\
& Female & 55 & 40 & 25 \\
\hline
\end{tabular}
(b) [10 marks] Fit a multinomial regression model with main effects for treatment and sex as well the interaction terms using R. Please provide R codes.