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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 …

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
• 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
• 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
• 14. Multi-Variable Linear Regression
Forecasting Steps
Set an objective
Build model
Evaluate model
Use model
4
• 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
• 21. Multi-Variable Linear Regression
Example: Retail Sales
6
• 22. Multi-Variable Linear Regression
Selecting Independent Variables
• Time
• 23. Captures time in 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
7
• 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
• 39. Multi-Variable Linear Regression
Build Model
• Software finds us the best fit line to the data; minimizing the sum of squared errors
9
• 40. Multi-Variable Linear Regression
Evaluate Model
10
• 51. Multi-Variable Linear Regression
ExampleDescriptive Statistics
11
• 57. Multi-Variable Linear Regression
ExampleAccuracy / Error
12
• 66. Multi-Variable Linear Regression
ExampleStatistical Significance
13
• 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
• 79. Multi-Variable Linear Regression
Coefficient Analysis Example
15
• 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