Multi-Variable Linear Regression<br />Lesson #6<br />Multi-Variable Linear Regression<br />Method<br />1<br />Copyright 20...
Multi-Variable Linear Regression<br />Model Introduction<br /><ul><li>An expansion on the linear regression method
Estimates a linear equation based upon multiple independent variables, not just one, i.e. time
Uses the estimated linear equation to forecast future values
Method format:
Y = a + b × x1 + c × x2 + d × x3 + …</li></ul>2<br />Copyright 2010 DeepThought, Inc.<br />
Multi-Variable Linear Regression<br />Model Details<br /><ul><li>Method characteristics
Fits a linear equation to data
Estimating a linear equation which minimizes the errors between actual data points and model estimates
When to use method
More then one variable impacting the dependent variable
When not to use
Creating simple models</li></ul>3<br />Copyright 2010 DeepThought, Inc.<br />
Multi-Variable Linear Regression<br />Forecasting Steps<br />Set an objective<br />Build model<br />Evaluate model<br />Us...
Multi-Variable Linear Regression<br />Objective Setting<br /><ul><li>Simpler is better
Multi-linear regression allows to test whether a line through each of the independent variablesworks as a model. Objective...
Example objectives for retail sales (see next slide):
Test if retail sales can be fit to a multivariable linear regression model
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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
  24. 24. Adds time variable to 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
  32. 32. Adds an economic variable to your model</li></ul>7<br />Copyright 2010 DeepThought, Inc.<br />
  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
  47. 47. R2; Adjusted R2
  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%
  63. 63. R2; Adjusted R2
  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
  83. 83. Answer objectives</li></ul>17<br />Copyright 2010 DeepThought, Inc.<br />
  84. 84. Multi-Variable Linear Regression<br />Example<br /><ul><li>Forecasts</li></ul>18<br />Copyright 2010 DeepThought, Inc.<br />
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