This lesson begins with explaining the multi-variable linear regression method characteristics, and uses. Multi-variable linear regression method attempts to best fit a line through each of the independent variables and the dependent variable. Using an example and the forecasting process, we apply the multi-variable linear regression method method to create a model and forecast based upon it.

1. Multi-Variable Linear Regression Lesson #6 Multi-Variable Linear Regression Method 1 Copyright 2010 DeepThought, Inc.

3. Estimates a linear equation based upon multiple independent variables, not just one, i.e. time

4. Uses the estimated linear equation to forecast future values

5. Method format:

6. Y = a + b × x1 + c × x2 + d × x3 + …2 Copyright 2010 DeepThought, Inc.

8. Fits a linear equation to data

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

10. When to use method

11. More then one variable impacting the dependent variable

12. When not to use

13. Creating simple models3 Copyright 2010 DeepThought, Inc.

14. Multi-Variable Linear Regression Forecasting Steps Set an objective Build model Evaluate model Use model 4 Copyright 2010 DeepThought, Inc.

16. Multi-linear regression allows to test whether a line through each of the independent variablesworks as a model. Objectives should take that principal under consideration

17. Example objectives for retail sales (see next slide):

18. Test if retail sales can be fit to a multivariable linear regression model

19. If independent variables exhibits a statistically significant fit, review and interpret results

20. If model looks good, create a forecast based off model5 Copyright 2010 DeepThought, Inc.

21. Multi-Variable Linear Regression Example: Retail Sales 6 Copyright 2010 DeepThought, Inc.

23. Captures time in your model

24. Adds time variable to your model

25. Dummy Variables

26. Captures seasonality in your model

27. Adds dummy variables for each of the seasons, except for one which is the base season. In our case it will always be the first season such as January for monthly data

28. Economic Variables

29. Captures an economic relationship in your model

30. Can add any variable from the database to your model

31. Follow economic, financial, or other theory/assumptions as to why you added that specific independent variable

32. Adds an economic variable to your model7 Copyright 2010 DeepThought, Inc.

34. Dummy variables (seasonal indices)

35. Independent variables:

36. POP (U.S. Population)

37. PCEPILFE (Personal Consumption Expenditures)

38. CP (Corporate Profits)8 Copyright 2010 DeepThought, Inc.

41. Mean

42. Variance & Standard Deviation

43. Accuracy / Error

44. SSE

45. RMSE

46. MAPE

47. R2; Adjusted R2

48. Statistical Significance

49. F-Test

50. P-Value F-Test10 Copyright 2010 DeepThought, Inc.

52. 245757.97

53. Variance

54. 39156435.51

55. Standard Deviation

56. 6257.51 11 Copyright 2010 DeepThought, Inc.

58. 2740950485.42

59. RMSE

60. 6213.29

61. MAPE

62. 2%

63. R2; Adjusted R2

64. 99%

65. 99%12 Copyright 2010 DeepThought, Inc.

67. 784.79

68. P-Value F-Test

69. 0.0013 Copyright 2010 DeepThought, Inc.

71. The deviation of observations of the coefficient from its mean

72. T-Test

73. Test whether there is a statistical difference between the coefficient and a zero coefficient, higher the value the higher the confidence

74. T-Test P-Value

75. Represents the percentage of significance of the T-Test

76. The lower the T-Test P-Value, the lower the percent that the coefficient is wrongfully assumed to be different from a zero coefficient

77. 1 – p-value = Significance Level of the Coefficient (%)

78. Significance level of the coefficient (%) represents the amount of confidence we have that the coefficient is different from zero14 Copyright 2010 DeepThought, Inc.

79. Multi-Variable Linear Regression Coefficient Analysis Example 15 Copyright 2010 DeepThought, Inc.

81. Will use accuracy/error statistics to compare multiple models to find best models16 Copyright 2010 DeepThought, Inc.

83. Answer objectives17 Copyright 2010 DeepThought, Inc.