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# ForecastIT 6. Multi-Variable Linear Regression

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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.

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### ForecastIT 6. Multi-Variable Linear Regression

1. 1. Multi-Variable Linear Regression<br />Lesson #6<br />Multi-Variable Linear Regression<br />Method<br />1<br />Copyright 2010 DeepThought, Inc.<br />
2. 2. Multi-Variable Linear Regression<br />Model Introduction<br /><ul><li>An expansion on the linear regression method
3. 3. Estimates a linear equation based upon multiple independent variables, not just one, i.e. time
4. 4. Uses the estimated linear equation to forecast future values
5. 5. Method format:
6. 6. Y = a + b × x1 + c × x2 + d × x3 + …</li></ul>2<br />Copyright 2010 DeepThought, Inc.<br />
7. 7. Multi-Variable Linear Regression<br />Model Details<br /><ul><li>Method characteristics
8. 8. Fits a linear equation to data
9. 9. Estimating a linear equation which minimizes the errors between actual data points and model estimates
10. 10. When to use method
11. 11. More then one variable impacting the dependent variable
12. 12. When not to use
13. 13. Creating simple models</li></ul>3<br />Copyright 2010 DeepThought, Inc.<br />
14. 14. Multi-Variable Linear Regression<br />Forecasting Steps<br />Set an objective<br />Build model<br />Evaluate model<br />Use model<br />4<br />Copyright 2010 DeepThought, Inc.<br />
15. 15. Multi-Variable Linear Regression<br />Objective Setting<br /><ul><li>Simpler is better
16. 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. 17. Example objectives for retail sales (see next slide):
18. 18. Test if retail sales can be fit to a multivariable linear regression model
19. 19. If independent variables exhibits a statistically significant fit, review and interpret results
20. 20. If model looks good, create a forecast based off model</li></ul>5<br />Copyright 2010 DeepThought, Inc.<br />
21. 21. Multi-Variable Linear Regression<br />Example: Retail Sales<br />6<br />Copyright 2010 DeepThought, Inc.<br />
22. 22. Multi-Variable Linear Regression<br />Selecting Independent Variables<br /><ul><li>Time
23. 23. Captures time in your model
25. 25. Dummy Variables
26. 26. Captures seasonality in your model
27. 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. 28. Economic Variables
29. 29. Captures an economic relationship in your model
30. 30. Can add any variable from the database to your model
31. 31. Follow economic, financial, or other theory/assumptions as to why you added that specific independent variable
33. 33. Multi-Variable Linear Regression<br />Picking Independent Variables<br /><ul><li>Time
34. 34. Dummy variables (seasonal indices)
35. 35. Independent variables:
36. 36. POP (U.S. Population)
37. 37. PCEPILFE (Personal Consumption Expenditures)
38. 38. CP (Corporate Profits)</li></ul>8<br />Copyright 2010 DeepThought, Inc.<br />
39. 39. Multi-Variable Linear Regression<br />Build Model<br /><ul><li>Software finds us the best fit line to the data; minimizing the sum of squared errors</li></ul>9<br />Copyright 2010 DeepThought, Inc.<br />
40. 40. Multi-Variable Linear Regression<br />Evaluate Model<br /><ul><li>Descriptive Statistics
41. 41. Mean
42. 42. Variance & Standard Deviation
43. 43. Accuracy / Error
44. 44. SSE
45. 45. RMSE
46. 46. MAPE
48. 48. Statistical Significance
49. 49. F-Test
50. 50. P-Value F-Test</li></ul>10<br />Copyright 2010 DeepThought, Inc.<br />
51. 51. Multi-Variable Linear Regression<br />ExampleDescriptive Statistics<br /><ul><li>Mean
52. 52. 245757.97
53. 53. Variance
54. 54. 39156435.51
55. 55. Standard Deviation
56. 56. 6257.51 </li></ul>11<br />Copyright 2010 DeepThought, Inc.<br />
57. 57. Multi-Variable Linear Regression<br />ExampleAccuracy / Error<br /><ul><li>SSE
58. 58. 2740950485.42
59. 59. RMSE
60. 60. 6213.29
61. 61. MAPE
62. 62. 2%
64. 64. 99%
65. 65. 99%</li></ul>12<br />Copyright 2010 DeepThought, Inc.<br />
66. 66. Multi-Variable Linear Regression<br />ExampleStatistical Significance<br /><ul><li>F-Test
67. 67. 784.79
68. 68. P-Value F-Test
69. 69. 0.00</li></ul>13<br />Copyright 2010 DeepThought, Inc.<br />
70. 70. Multi-Variable Linear Regression<br />Coefficient Statistical Significance<br /><ul><li>Standard Error (SE)
71. 71. The deviation of observations of the coefficient from its mean
72. 72. T-Test
73. 73. Test whether there is a statistical difference between the coefficient and a zero coefficient, higher the value the higher the confidence
74. 74. T-Test P-Value
75. 75. Represents the percentage of significance of the T-Test
76. 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. 77. 1 – p-value = Significance Level of the Coefficient (%)
78. 78. Significance level of the coefficient (%) represents the amount of confidence we have that the coefficient is different from zero</li></ul>14<br />Copyright 2010 DeepThought, Inc.<br />
79. 79. Multi-Variable Linear Regression<br />Coefficient Analysis Example<br />15<br />Copyright 2010 DeepThought, Inc.<br />
80. 80. Multi-Variable Linear Regression<br />Compare Multiple Models<br /><ul><li>Skip this step until have knowledge of multiple methods
81. 81. Will use accuracy/error statistics to compare multiple models to find best models</li></ul>16<br />Copyright 2010 DeepThought, Inc.<br />
82. 82. Multi-Variable Linear Regression<br />Use Model<br /><ul><li>Understand limitations of model