Forecasting Time Series & Simple Linear Regression

1. Given the following demand for antibiotics from patients attending a local clinic, please generate forecasts by arithmetic mean, last period value, MA (3), MA (5), ES (0.1), ES (0.4), and ES (0.9). Please calculate MAD and MSE for each forecasting method. Which forecasting method performs the best, the worst? Please answer in Excel for your solutions.

Week t	Dt
1	88
2	88
3	97
4	83
5	91
6	93
7	73
8	85
9	92
10	87

2 .Bruce managing the dialysis equipment sales department for Fresenius. He is reviewing the sales records for the South West region in the U.S. Based on the sales records data in the table, answering the following questions: Please answer in Excel for your solutions.

Weeks	Sales
1	33
2	31
3	31
4	37
5	40
6	33
7	50
8	45
9	55
10	60

2-a. Bruce wants to prepare for future sales. Please make the forecast, based on historical data, for sales in weeks 11 and 12, using the following methods: moving average (3), moving average (4), moving average (5), exponential smoothing (0.1), exponential smoothing (0.4), exponential smoothing (0.8). Plot the demand and forecasts in scatter plots. Compare the mean absolution deviation (MAD) and bias among these methods.

2-b. Please make a forecast using simple linear regression. What is the model? Is the model valid (residual analysis)? What is the significance of the regression model (R², p-value of the slope)?

2-c. Compare the smoothing methods with the regression. Which method would you recommend? Why?