Forecasting Demand

A new production manager for a hardware company needs to find the best forecasting technique for their line of electric drills. They have collected data regarding sales over 12 years, the price/unit, and advertising expenditures/year. They want to deploy time series techniques as well as "causal" models using multiple regression to decide which can predict/forecast sales for next year. They would like to minimize forecasting errors: bias, MAD, MSE, RMSE, MAPE, and tracking signal.

Year Sales/unit (Thousands) Price/Unit Advertising ($000)

1 400 280 600

2 700 215 835

3 900 211 1,100

4 1,300 210 1,400

5 1,150 215 1,200

6 1,200 200 1,300

7 900 225 900

8 1,100 207 1,100

9 980 220 700

10 1,234 211 900

11 925 227 700

12 800 245 690

1. Use multiple regression with price/unit and advertising as independent variables. (Y Sales, X Advertising)
   1. Is this a good model substantively and statistically? Document your response. (1 Point)
   2. Forecast for periods 1-13 using multiple regression analysis. For period 13, use a price of $300 and advertising expenditures of $900 (in thousands).
   3. Which variable, price or advertising, has a larger effect on sales and how do you know. Document your work.
   4. Plot sales and the forecasted values on the same figure using Multiple Regression. Provide some commentary based on what you see.
   5. Calculate: bias, MAD, MSE, RMSE, MAPE, and track tracking signal. Also, plot the tracking signal and comment on what you see on the plot.
2. Based on a three-period, exponential smoothing and multiple regression, which model would you use and why?

Please show your work and explain how you arrived at your answer.