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 …

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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  • 1. Multi-Variable Linear Regression
    Lesson #6
    Multi-Variable Linear Regression
    Method
    1
    Copyright 2010 DeepThought, Inc.
  • 2. Multi-Variable Linear Regression
    Model Introduction
    • An expansion on the linear regression method
    • 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.
  • 7. Multi-Variable Linear Regression
    Model Details
    • Method characteristics
    • 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 models
    3
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  • 14. Multi-Variable Linear Regression
    Forecasting Steps
    Set an objective
    Build model
    Evaluate model
    Use model
    4
    Copyright 2010 DeepThought, Inc.
  • 15. Multi-Variable Linear Regression
    Objective Setting
    • Simpler is better
    • 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 model
    5
    Copyright 2010 DeepThought, Inc.
  • 21. Multi-Variable Linear Regression
    Example: Retail Sales
    6
    Copyright 2010 DeepThought, Inc.
  • 22. Multi-Variable Linear Regression
    Selecting Independent Variables
    • Time
    • 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 model
    7
    Copyright 2010 DeepThought, Inc.
  • 33. Multi-Variable Linear Regression
    Picking Independent Variables
    • Time
    • 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.
  • 39. Multi-Variable Linear Regression
    Build Model
    • Software finds us the best fit line to the data; minimizing the sum of squared errors
    9
    Copyright 2010 DeepThought, Inc.
  • 40. Multi-Variable Linear Regression
    Evaluate Model
    10
    Copyright 2010 DeepThought, Inc.
  • 51. Multi-Variable Linear Regression
    ExampleDescriptive Statistics
    11
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  • 57. Multi-Variable Linear Regression
    ExampleAccuracy / Error
    12
    Copyright 2010 DeepThought, Inc.
  • 66. Multi-Variable Linear Regression
    ExampleStatistical Significance
    13
    Copyright 2010 DeepThought, Inc.
  • 70. Multi-Variable Linear Regression
    Coefficient Statistical Significance
    • Standard Error (SE)
    • 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 zero
    14
    Copyright 2010 DeepThought, Inc.
  • 79. Multi-Variable Linear Regression
    Coefficient Analysis Example
    15
    Copyright 2010 DeepThought, Inc.
  • 80. Multi-Variable Linear Regression
    Compare Multiple Models
    • Skip this step until have knowledge of multiple methods
    • 81. Will use accuracy/error statistics to compare multiple models to find best models
    16
    Copyright 2010 DeepThought, Inc.
  • 82. Multi-Variable Linear Regression
    Use Model
    • Understand limitations of model
    • 83. Answer objectives
    17
    Copyright 2010 DeepThought, Inc.
  • 84. Multi-Variable Linear Regression
    Example
    • Forecasts
    18
    Copyright 2010 DeepThought, Inc.