This lesson begins with explaining the linear regression method characteristics, and uses. Linear regression method attempts to best fit a line through the data. Using an example and the forecasting process, we apply the linear regression method to create a model and forecast based upon it.

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.

5. Method format:

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

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 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

37. Statistical Significance

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

49. Standard Deviation

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

87. Answer objectives

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