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ForecastIT 2. Linear Regression & Model Statistics
- 1. Linear Regression and Model Statistics Lesson #2 Linear Regression Method Copyright 2010 DeepThought, Inc. 1
- 3. Estimates a line through the data
- 4. Uses the estimated line equation to forecast future values.
- 6. Y = a + b × tCopyright 2010 DeepThought, Inc. 2
- 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
- 13. When not to use
- 14. Estimate anything beyond a simple linear relationship Copyright 2010 DeepThought, Inc. 3
- 15. Linear Regression and Model Statistics Forecasting Steps Set an objective Build model Evaluate model Use model Copyright 2010 DeepThought, Inc. 4
- 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 Statistics Example: M2 Money Stock Copyright 2010 DeepThought, Inc. 6
- 24. Adjust time frame, units, periods to forecast as needed
- 25. Determine if linear regression is a possible candidate based on method characteristics
- 26. Determine if transforming the units will enable use of model
- 27. Eight different unit transformation techniquesCopyright 2010 DeepThought, Inc. 7
- 30. Mean
- 31. Variance & Standard Deviation
- 32. Accuracy / Error
- 33. SSE
- 34. RMSE
- 35. MAPE
- 36. R2; Adjusted R2
- 38. F-Test
- 39. P-Value F-TestCopyright 2010 DeepThought, Inc. 9
- 42. Estimates the variation the data exhibits from the mean
- 43. Standard deviation is the squared root of the variance
- 44. Used to measure the distribution of the variable away from the mean, most observations of the variable will be within ± 3 standard deviationsCopyright 2010 DeepThought, Inc. 11
- 46. 4214.38
- 47. Variance
- 48. 3346475.10
- 50. 1829.34 Copyright 2010 DeepThought, Inc. 12
- 52. Sums the errors between the actual values and model values
- 53. Measures the total error of the model
- 54. M2 Example:
- 55. SSE: 316778645.89 Copyright 2010 DeepThought, Inc. 13
- 57. An averaged out total of errors based upon the number of observations
- 58. Simple way to compare models based on error
- 59. M2 Example:
- 60. RMSE: 456.82 Copyright 2010 DeepThought, Inc. 14
- 62. Describes the average percentage of variation exhibited between actual and forecasted values
- 63. M2 Example:
- 64. MAPE: 10.09% Copyright 2010 DeepThought, Inc. 15
- 66. Measures the percentage of variation captured by the model
- 67. Adjusted R2incorporated the number of variables used and sample size to adjust the R2 valueCopyright 2010 DeepThought, Inc. 16
- 69. 93.76%
- 70. Adjusted R2
- 71. 93.76% Copyright 2010 DeepThought, Inc. 17
- 73. Used to test if model build is statistically significant from being equal to zero
- 74. The larger the F-test the betterCopyright 2010 DeepThought, Inc. 18
- 76. 1 – p-value = Significance Level of the Model (%)
- 77. Significance level of the model (%) represents the amount of confidence we have that our model is different from a model with no impact, or zero impactCopyright 2010 DeepThought, Inc. 19
- 79. 22778.98
- 80. F-Test P-Value
- 81. 0.00 Copyright 2010 DeepThought, Inc. 20
- 83. Will use accuracy/error statistics to compare multiple models to find best modelsCopyright 2010 DeepThought, Inc. 21
- 85. Only measures a trend
- 86. A long term average
- 88. Does M2 has a linear trend
- 89. If trend exists, what is its magnitude
- 90. If model statistically significant, forecastCopyright 2010 DeepThought, Inc. 22
- 92. Next Period is 1519
- 93. Forecast for that period is:
- 94. Y = 1145.31 + 4.04 × 1519Y = 7283.446866 Copyright 2010 DeepThought, Inc. 23