1. © Copyright 2001, Alan Marshall1 Regression Analysis Time Series Analysis

2. © Copyright 2001, Alan Marshall2 Regression Analysis è A statistical technique for determining the best fit line through a series of data

3. © Copyright 2001, Alan Marshall3 Error è No line can hit all, or even most of the points - The amount we miss by is called ERROR è Error does not mean mistake! It simply means the inevitable “missing” that will happen when we generalize, or try to describe things with models è When we looked at the mean and variance, we called the errors deviations

4. © Copyright 2001, Alan Marshall4 What Regression Does è Regression finds the line that minimizes the amount of error, or deviation from the line è The mean is the statistic that has the minimum total of squared deviations è Likewise, the regression line is the unique line that minimizes the total of the squared errors. è The Statistical term is “Sum of Squared Errors” or SSE

5. © Copyright 2001, Alan Marshall5 Example è Suppose we are examining the sale prices of compact cars sold by rental agencies and that we have the following summary statistics:

6. © Copyright 2001, Alan Marshall6 Summary Statistics è Our best estimate of the average price would be $5,411 è Our 95% Confidence Interval would be $5,411 ± (2)(255) or $5,411 ± (510) or $4,901 to $5,921

7. © Copyright 2001, Alan Marshall7 Something Missing? è Clearly, looking at this data in such a simplistic way ignores a key factor: the mileage on the vehicle

8. © Copyright 2001, Alan Marshall8 Price vs. Mileage

9. © Copyright 2001, Alan Marshall9 Importance of the Factor è After looking at the scatter graph, you would be inclined to revise you estimate depending on the mileage u 25,000 km about $5,700 - $5,900 u 45,000 km about $5,100 - $5,300 è Similar to getting new test information in decision theory.

10. © Copyright 2001, Alan Marshall10 Switch to Excel File CarPrice.xls Tab Odometer

11. © Copyright 2001, Alan Marshall11 The Regression Tool è Tools u Data Analysis ä Choose “Regression” from the dialogue box menu.

12. © Copyright 2001, Alan Marshall12 More Than You Need

13. © Copyright 2001, Alan Marshall13 Ignore è The ANOVA table è The Upper 95% and Lower 95% stuff.

14. © Copyright 2001, Alan Marshall14

15. © Copyright 2001, Alan Marshall15 Stripped Down Output

16. © Copyright 2001, Alan Marshall16 Interpretation è Our estimated relationship is è Price = $6,533 - 0.031(km) u Every 1000 km reduces the price by an average of $31 u What does the $6,533 mean? ä Careful! It is outside the data range!

17. © Copyright 2001, Alan Marshall17 Quality è The model makes sense: Price is lowered as mileage increases, and by a plausible amount.  The slope: 13.5  from 0! u Occurs randomly, or by chance, with a probability that has 23 zeros! è The R-squared: 0.65: 65% of the variation in price is explained by mileage

18. © Copyright 2001, Alan Marshall18 Multiple Regression Using More than One Explanatory Variable

19. © Copyright 2001, Alan Marshall19 Using Excel è No significant changes

20. © Copyright 2001, Alan Marshall20 To Watch For è Variables significantly related to each other u Correlation Function (Tools Data Analysis) u Look for values above 0.5 or below -0.5 è Nonsensical Results u Wrong Signs è Weak Variables u Magnitude of the T-ratio less than 2 u p-value greater than 0.05

21. © Copyright 2001, Alan Marshall21 Dummy Variables è Qualitative variables that allow the relationship to shift is a certain factor is present. è Illustrated in the two upcoming examples

22. © Copyright 2001, Alan Marshall22 Examples House Prices Theme Park Attendance

23. © Copyright 2001, Alan Marshall23 Time Series Analysis

24. © Copyright 2001, Alan Marshall24 Time Series Analysis è Various techniques that allow us to u Understand the variation in a time series u Understand the seasonalities and cycles in a time series u Use this understanding to make predictions

25. © Copyright 2001, Alan Marshall25 Two Techniques è Deseasonalizing based on a moving average è Using Dummy Variables to Isolate the seasonal effects.

26. © Copyright 2001, Alan Marshall26 Moving Average è Calculate a moving average è Calculate the ratio of the observation to the moving average è Collect all ratios organized by the point in the seasonal cycle u months, if monthly; quarters, if quarterly è Average, and adjust if necessary, to get seasonal adjustment factors

27. © Copyright 2001, Alan Marshall27 Example Course Kit Example Page 143

28. © Copyright 2001, Alan Marshall28 Regression è Add dummy variables for all but one seasonal period (i.e., 3 for quarterly, 11 for monthly)

29. © Copyright 2001, Alan Marshall29 Example Revisit the Course Kit Example Page 143

30. © Copyright 2001, Alan Marshall30 Edgar Feidler’s Six Rules of Forecasting With thanks to Peter Walker for bringing this to my attention

31. © Copyright 2001, Alan Marshall31 Forecasting is very difficult, especially if it is about the future

32. © Copyright 2001, Alan Marshall32 The minute you make a forecast, you know you’re going to be wrong, you just don’t know when or in what direction.

33. © Copyright 2001, Alan Marshall33 The herd instinct among forecasters make sheep look like independent thinkers

34. © Copyright 2001, Alan Marshall34 When asked to explain a forecast, never underestimate the power of a platitude

35. © Copyright 2001, Alan Marshall35 When you know absolutely nothing about a subject, you can still do a forecast by asking 300 people who don’t know anything either. That’s called a survey

36. © Copyright 2001, Alan Marshall36 Forecasters learn more and more about less and less until they know nothing about anything