Each year Dr. Jerry Hep organizes a road cycling fundraiser for the hospital he works at. The money is raised from the fees charged to each rider to participate less costs such as having policing at busy intersections and participant mementos. A new sponsor has come on board who will also manage the operations of the ride. Having no prior experience, this sponsor created a website for riders to register but did not add a payment feature. Fees would be paid on the morning of the ride. This year's memento is an expensive European cycling jersey. Jerry tells the sponsor they could have a problem. They have to pre-order the jerseys from the supplier for the number of registered riders but won't collect the money until the morning of the ride. This arrangement also encourages riders to not register but just show up the morning of the ride. The sponsor wants to know why that is a problem. Jerry tells the sponsor that if it rains, they can expect to have many riders not show up and be stuck with many jerseys. The cost of the jerseys left over will come out of the fundraising profits.

To minimize losses, the sponsor plans to order jerseys based on an assumption it will rain. Most jerseys ordered in the past were for unisex large. Jerry provides the sponsor with the following data for years that it rained. Since the ride occurs in early May, there have been many rainy rides.

Year Orders Large Unisex Jersey

2001 150

2003 158

2005 165

2007 180

2009 195

2012 207

2014 215

2015 222

a) Calculate the projected demand for large unisex jerseys for 2016 assuming it will rain using the least squares trend equation. You must the formulas used and all calculations. (5 marks)

b) Jerry wants to know error related to the projected number of riders ordering a large unisex jersey. Calculate the standard error of the regression computed in part a and the standard error to project a probability for a range of jerseys ordered. You must show all the formulas used and all calculations. (5 marks)