A convenience store recently started to carry a new brand of soft drink. Management is interested in estimating future sales volume to determine whether it should continue to carry the new brand or replace it with another brand. The following table provides the number of cans sold per week. Use both the trend projection with regression and the exponential smoothing (let alpha =0.4) with an initial forecast for week 1 of 569) methods to forecast demand for week 13. Compare these methods by using the mean absolute deviation and mean absolute percent error performance criteria. Does your analysis suggest that sales are trending and if so, by how much?

Period 1 2 3 4 5 6 7 8 9 10 11 12 Sales 569 615 645 742 640 606 732 718 713 690 678 738 Observation 1 2 3 4 5 6 7 8 9 10 11 12

(i) Obtain the trend projection with regression forecast.

The forecast for week 13 is

Week 13 corresponds to t=13. Obtain the forecast for the next week by substituting t=13 into the regression equation.

(ii) Now obtain the exponential smoothing forecast.

The exponential smoothing method is a weighted moving average method that calculates the average of a time series by giving recent demands more weight than earlier demands. The equation for the forecast is:

Ft+1=(Demand this period)+(1)(Forecast calculated last period)=Dt+(1)Ft.