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QUESTION $2.[40$ points$]$ Recent medical errors at Benson Memorial Hospital have resulted in the development of an extensive Patient Safety Improvement Program, led by patient safety officers who are responsible for analysing trends and identifying opportunities for improving patient safety. A key element of this program is ensuring adequate staff are available to provide care. In order to develop such staffing models, the hospital must be able to predict patient inflows at a more granular level. Table II depicts patient admissions data for Benson Memorial's intensive care unit $2.$a$.$ Develop a linear regression model using this daily$/$monthly patient admissions data to predict the inflow of patient admissions. $2.$b$.$ Predict admissions for January, February, and March of the following year. $2.$c$.$ Develop monthly and daily indexes for patient admissions. $2.$d$.$ Using the daily indexes technique, develop the monthly adjusted predictions for January, February, and March as well as for Monday through Friday in these months. $2.$e$.$ Analyse the regression model and adjusted predictions developed in part $($d$).$ Provide the chair of the Patient Safety Improvement Program a brief summary of your findings to aid in the development of a revised staffing model, providing some insight into the predicted inflows of patient admissions. $($Hint: Look at predicted patient admissions during each day of the week as well as overall trends in admissions.$)$

Table II depicts patient admissions data for Benson Memorial's intensive care unit.

Month$/$Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday January $42424039373745$ February $43454548494446$ March $47495760594650$ April $57556159596566$ May $80727567676366$ June $64627183786963$ July $80626364678182$ August $41555963494646$ September $40444551635542$ October $42444339443949$ November $49526660515550$ December $58545861767363$ Grand Total $643636683694699673668$

Table II