1. Review Use data table from Quiz #4 to forecast sales using exponential smoothing, α = 0.2 What is α called? We are weighting the error associated with each time period by α 1 Y t – F t = e t

2. Review 2

3. Solve F 2, F 3, … F 7 and e 2, e 3, … e 6 3

4. Review 4

5. Use data table from Quiz #4 to forecast sales using simple linear regression We are using ONLY a time variable to predict sales here! Predict future sales based on correlation between time (X, independent variable) and sales (Y, dependent variable) 5

6. Review 6

7. Calculate MSE for the forecast, and calculate T 7 7

8. Review 8

9. 9

10. 10

11. Seasonal pattern no trend 11 Year 1Year 2Year 3Year 4Year 5

12. Seasonal pattern no trend We are saying that umbrella sales are driven by seasonal variability with NO increasing or decreasing trend over time Every year: 1 st and 3 rd quarters have moderate sales 2 nd quarter has highest sales 4 th quarter has lowest sales 12

13. Seasonal pattern no trend If we are using a linear trend to forecast (simple linear regression), we can introduce “season” as a independent categorical variables (X’s) In statistics, a categorical variable is a variable that can take on a very limited, fixed number of possible values 13

14. Seasonal pattern no trend If k = the # of categories, you will need k – 1 dummy variables Since there are four seasons (4 categories), we need three dummy variables Qtr1 = 1 if Quarter 1, 0 otherwise Qtr2 = 1 if Quarter 2, 0 otherwise Qtr3 = 1 if Quarter 3, 0 otherwise 14

15. Seasonal pattern no trend 15 Dummy or categorical variables for seasonal Effects Q1 = 1 if quarter = 1, otherwise Q1 = 0 Q2 = 1 if quarter = 2, otherwise Q2 = 0 Q3 = 1 if quarter = 3, otherwise Q3 = 0 Q4 = 0

16. Seasonal pattern no trend 16

17. Seasonal pattern no trend What is our model? 17

18. Seasonal pattern no trend Predict sales in each quarter of year 6 using the model 18

19. Seasonal pattern with trend 19

20. Seasonal pattern with trend We are saying that tie sales are driven by seasonal variability and that there is an increasing trend in sales over time Every year: Sales are lowest – by far – in 3 rd season Sales are highest in 1 st season 20

21. Seasonal pattern with trend 3 seasons or 3 categories ( k = 3) require the use of 2 dummy variables (k – 1) Seas1 t = 1 if Season 1 in time period t, 0 otherwise Seas2 t = 1 if Season 2 in time period t, 0 otherwise We will also need a time variable to address the trend over time 21

22. Seasonal pattern with trend 22 Dummy or categorical variables for seasonal Effects S1 = 1 if season = 1, otherwise S1 = 0 S2 = 1 if season = 2, otherwise S2 = 0 Time period variable

23. Seasonal pattern with trend 23

24. Seasonal pattern no trend What is our model? 24

25. Seasonal pattern no trend Predict sales in each season of year 5 using the model 25