This document discusses the linear regression method for forecasting, outlining its characteristics, when to use it, and steps for building and evaluating a model. It provides a detailed example using M2 money stock, illustrating objectives, model evaluation metrics like mean, variance, standard errors, and statistical significance. The document emphasizes the importance of understanding the limitations of linear regression and includes a forecasting example based on the constructed model.

1. Linear Regression and Model StatisticsLesson #2Linear Regression MethodCopyright 2010 DeepThought, Inc.1

2. Linear Regression and Model StatisticsMethod IntroductionOne of the simpler methods to use for forecasting

3. Estimates a line through the data

4. Uses the estimated line equation to forecast future values.

5. Method format:

6. Y = a + b × tCopyright 2010 DeepThought, Inc.2

7. Linear Regression and Model StatisticsModel CharacteristicsMethod characteristics

8. Fits a line to the data

9. Estimating a line which minimizes the errors between actual data points and model estimates

10. When to use method

11. Estimate trend

12. Estimate trend magnitude

13. When not to use

14. Estimate anything beyond a simple linear relationship Copyright 2010 DeepThought, Inc.3

15. Linear Regression and Model StatisticsForecasting StepsSet an objectiveBuild modelEvaluate modelUse modelCopyright 2010 DeepThought, Inc.4

16. Linear Regression and Model StatisticsObjective SettingSimpler is better

17. Linear regression allows to test whether a line fitted to the data works as a model. Objectives should take that principal under consideration

18. Example objectives for M2 Money Stock (see next slide):

19. Test if M2 has a linear trend over time

20. If M2 exhibits a statistically significant trend, review and interpret results

21. If model looks good, create a forecast based off modelCopyright 2010 DeepThought, Inc.5

22. Linear Regression and Model StatisticsExample: M2 Money StockCopyright 2010 DeepThought, Inc.6

23. Linear Regression and Model StatisticsMethod SelectionObserve time series qualities: trend, seasonality, cyclicality, and randomness