The manager of a tire store in Minneapolis has been concerned with the high cost of inventory. The current policy is to stock all the snow tires that are predicted to sell over the entire winter at the beginning of the season (end of October). The manager can reduce inventory costs by having suppliers deliver snow tires regularly from October to February. However, he needs to be able to predict weekly sales to avoid stockouts that will ultimately lose sales. To help develop a forecasting model, he records the number of snow tires sold weekly during the last winter and the amount of snowfall (in inches) in each week.

a.      Develop a regression model and use a software package to produce the statistics.

b.      Perform a complete diagnostic analysis to determine whether the required conditions are satisfied.

c.      If one or more conditions are unsatisfied, attempt to remedy the problem.

d.      Use whatever procedures you wish to assess how well the new model fits the data.

e.      Interpret and test each of the coefficients.