: Create a time series model $($with level, linear trend, and seasonal components$)$ for purposes of forecasting

daily demand at Penguin for April $9-27,$ including a margin of uncertainty for each day$$s forecast. Note, assume that

forecast errors are normally distributed.

Calculate:

$$ Deseasonalization $($Deseas$)$

$$ D$-$Bar

$$ S$-$Bar

$$ Seasonal $($Seas$)$ Factor

$$ Forecast

$$ Absolute Error

$$ Slope

$$ Intercept

$$ Mean Absolute Deviation $($MAD$)$

$$ Margin of Uncertainty

$$ Upper and Lower Forecasts per day

Time Series Forecasting

Penguin Images Services is a US$-$based healthcare service provider, specializing in state$-$of$-$the$-$art medical imaging. The

imaging services they offer include MRI, MR Angiography $($MRA$),$ CT scan, $3$D Imaging, X$-$ray and Ultrasound. Their

business model is based on low cost but responsive service. They attempt to achieve this goal by maintaining a group of

radiologists who are paid to evaluate images and to be available during various periods when services are expected.

That is$,$ when on duty, each radiologist is paid a minimum amount even when service is not required. Labor costs are

minimized by hiring radiologists located in certain high quality but lower cost locations, mainly Indi.

The effectiveness of Penguin$$s service is affected a great deal by their ability to forecast demand. Penguin does not

require that patients make an appointment, because most patients were referred by their physician. These patients

necessitated service on short notice.

Penguin$$s location in Bainston, Rhode Island, is opened for customers Monday through Friday $(0800-1700)$ and Saturday

$(0800-1200).$ At this location, a short$-$term increase in demand for MRI image evaluation has occurred. This growth was

caused by the closing of the other major imaging service provider in Bainston. The increase in demand is expected to

continue over the next several weeks. Historical demand $($number of images by day$)$ is shown below and included on the

accompanying Excel file: