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Linear Regression and Model Statistics<br />Lesson #2<br />Linear Regression Method<br />Copyright 2010 DeepThought, Inc.<...
Linear Regression and Model Statistics<br />Method Introduction<br /><ul><li>One of the simpler methods to use for forecas...
Estimates a line through the data
Uses the estimated line equation to forecast future values.
Method format:
Y = a + b × t</li></ul>Copyright 2010 DeepThought, Inc.<br />2<br />
Linear Regression and Model Statistics<br />Model Characteristics<br /><ul><li>Method characteristics
Fits a line to the data
Estimating a line which minimizes the errors between actual data points and model estimates
When to use method
Estimate trend
Estimate trend magnitude
When not to use
Estimate anything beyond a simple linear relationship </li></ul>Copyright 2010 DeepThought, Inc.<br />3<br />
Linear Regression and Model Statistics<br />Forecasting Steps<br />Set an objective<br />Build model<br />Evaluate model<b...
Linear Regression and Model Statistics<br />Objective Setting<br /><ul><li>Simpler is better
Linear regression allows to test whether a line fitted to the data works as a model. Objectives should take that principal...
Example objectives for M2 Money Stock (see next slide):
Test if M2 has a linear trend over time
If M2 exhibits a statistically significant trend, review and interpret results
If model looks good, create a forecast based off model</li></ul>Copyright 2010 DeepThought, Inc.<br />5<br />
Linear Regression and Model Statistics<br />Example: M2 Money Stock<br />Copyright 2010 DeepThought, Inc.<br />6<br />
Linear Regression and Model Statistics<br />Method Selection<br /><ul><li>Observe time series qualities: trend, seasonalit...
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ForecastIT 2. Linear Regression & Model Statistics

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This lesson begins with explaining the linear regression method characteristics, and uses. Linear regression method attempts to best fit a line through the data. Using an example and the forecasting process, we apply the linear regression method to create a model and forecast based upon it.

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ForecastIT 2. Linear Regression & Model Statistics

  1. 1. Linear Regression and Model Statistics<br />Lesson #2<br />Linear Regression Method<br />Copyright 2010 DeepThought, Inc.<br />1<br />
  2. 2. Linear Regression and Model Statistics<br />Method Introduction<br /><ul><li>One of the simpler methods to use for forecasting
  3. 3. Estimates a line through the data
  4. 4. Uses the estimated line equation to forecast future values.
  5. 5. Method format:
  6. 6. Y = a + b × t</li></ul>Copyright 2010 DeepThought, Inc.<br />2<br />
  7. 7. Linear Regression and Model Statistics<br />Model Characteristics<br /><ul><li>Method characteristics
  8. 8. Fits a line to the data
  9. 9. Estimating a line which minimizes the errors between actual data points and model estimates
  10. 10. When to use method
  11. 11. Estimate trend
  12. 12. Estimate trend magnitude
  13. 13. When not to use
  14. 14. Estimate anything beyond a simple linear relationship </li></ul>Copyright 2010 DeepThought, Inc.<br />3<br />
  15. 15. Linear Regression and Model Statistics<br />Forecasting Steps<br />Set an objective<br />Build model<br />Evaluate model<br />Use model<br />Copyright 2010 DeepThought, Inc.<br />4<br />
  16. 16. Linear Regression and Model Statistics<br />Objective Setting<br /><ul><li>Simpler is better
  17. 17. Linear regression allows to test whether a line fitted to the data works as a model. Objectives should take that principal under consideration
  18. 18. Example objectives for M2 Money Stock (see next slide):
  19. 19. Test if M2 has a linear trend over time
  20. 20. If M2 exhibits a statistically significant trend, review and interpret results
  21. 21. If model looks good, create a forecast based off model</li></ul>Copyright 2010 DeepThought, Inc.<br />5<br />
  22. 22. Linear Regression and Model Statistics<br />Example: M2 Money Stock<br />Copyright 2010 DeepThought, Inc.<br />6<br />
  23. 23. Linear Regression and Model Statistics<br />Method Selection<br /><ul><li>Observe time series qualities: trend, seasonality, cyclicality, and randomness
  24. 24. Adjust time frame, units, periods to forecast as needed
  25. 25. Determine if linear regression is a possible candidate based on method characteristics
  26. 26. Determine if transforming the units will enable use of model
  27. 27. Eight different unit transformation techniques</li></ul>Copyright 2010 DeepThought, Inc.<br />7<br />
  28. 28. Linear Regression and Model Statistics<br />Build Model<br /><ul><li>Software finds us the best fit line to the data; minimizing the sum of squared errors</li></ul>Copyright 2010 DeepThought, Inc.<br />8<br />
  29. 29. Linear Regression and Model Statistics<br />Evaluate Model<br /><ul><li>Descriptive Statistics
  30. 30. Mean
  31. 31. Variance & Standard Deviation
  32. 32. Accuracy / Error
  33. 33. SSE
  34. 34. RMSE
  35. 35. MAPE
  36. 36. R2; Adjusted R2
  37. 37. Statistical Significance
  38. 38. F-Test
  39. 39. P-Value F-Test</li></ul>Copyright 2010 DeepThought, Inc.<br />9<br />
  40. 40. Linear Regression and Model Statistics<br />Descriptive StatisticsMean<br /><ul><li>The average value of the data set</li></ul> ×http://images.google.com/imgres?imgurl=http://www.cs.princeton.edu/introcs/11gaussian/images/stddev.png&imgrefurl=http://www.cs.princeton.edu/introcs/11gaussian/&usg=__7JZMBeSrlQKPfVL2YCVuV8HVXkY=&h=206&w=570&sz=18&hl=en&start=54&um=1&tbnid=5jb7PXr6kgP08M:&tbnh=48&tbnw=134&prev=/images%3Fq%3Dstandard%2Brandom%2Bdistribution%26ndsp%3D18%26hl%3Den%26client%3Dfirefox-a%26rls%3Dorg.mozilla:en-US:official%26hs%3DXpO%26sa%3DN%26start%3D36%26um%3D1<br />Copyright 2010 DeepThought, Inc.<br />10<br />
  41. 41. Linear Regression and Model Statistics<br />Variance & Standard Deviation<br /><ul><li>The sum of squared deviations of the data from the mean
  42. 42. Estimates the variation the data exhibits from the mean
  43. 43. Standard deviation is the squared root of the variance
  44. 44. Used to measure the distribution of the variable away from the mean, most observations of the variable will be within ± 3 standard deviations</li></ul>Copyright 2010 DeepThought, Inc.<br />11<br />
  45. 45. Linear Regression and Model Statistics<br />M2 Example<br /><ul><li>Mean
  46. 46. 4214.38
  47. 47. Variance
  48. 48. 3346475.10
  49. 49. Standard Deviation
  50. 50. 1829.34 </li></ul>Copyright 2010 DeepThought, Inc.<br />12<br />
  51. 51. Linear Regression and Model Statistics<br />Accuracy/ErrorSSE<br /><ul><li>Sum of Square Errors (SSE)
  52. 52. Sums the errors between the actual values and model values
  53. 53. Measures the total error of the model
  54. 54. M2 Example:
  55. 55. SSE: 316778645.89 </li></ul>Copyright 2010 DeepThought, Inc.<br />13<br />
  56. 56. Linear Regression and Model Statistics<br />RMSE<br /><ul><li>The square root of the sum of square error divided by the number of observations
  57. 57. An averaged out total of errors based upon the number of observations
  58. 58. Simple way to compare models based on error
  59. 59. M2 Example:
  60. 60. RMSE: 456.82 </li></ul>Copyright 2010 DeepThought, Inc.<br />14<br />
  61. 61. Linear Regression and Model Statistics<br />MAPE<br /><ul><li>The average percentage error of the model
  62. 62. Describes the average percentage of variation exhibited between actual and forecasted values
  63. 63. M2 Example:
  64. 64. MAPE: 10.09% </li></ul>Copyright 2010 DeepThought, Inc.<br />15<br />
  65. 65. Linear Regression and Model Statistics<br />R-Squared & Adjusted R-Squared<br /><ul><li>A proportion between unexplained and explained errors
  66. 66. Measures the percentage of variation captured by the model
  67. 67. Adjusted R2incorporated the number of variables used and sample size to adjust the R2 value</li></ul>Copyright 2010 DeepThought, Inc.<br />16<br />
  68. 68. Linear Regression and Model Statistics<br />M2 Example<br /><ul><li>R2
  69. 69. 93.76%
  70. 70. Adjusted R2
  71. 71. 93.76% </li></ul>Copyright 2010 DeepThought, Inc.<br />17<br />
  72. 72. Linear Regression and Model Statistics<br />Statistical SignificanceF-Test<br /><ul><li>A proportion between explained and unexplained errors of model
  73. 73. Used to test if model build is statistically significant from being equal to zero
  74. 74. The larger the F-test the better</li></ul>Copyright 2010 DeepThought, Inc.<br />18<br />
  75. 75. Linear Regression and Model Statistics<br /> F-Test P-Value<br /><ul><li>The F-Test P-Value represents</li></ul>the percentage of significance of the F-test (blue area on graph) <br /><ul><li>The higher the value of the F-test the lower the shaded blue area is. As the blue area decreases, confidence about our model being statistically significant increases
  76. 76. 1 – p-value = Significance Level of the Model (%)
  77. 77. Significance level of the model (%) represents the amount of confidence we have that our model is different from a model with no impact, or zero impact</li></ul>Copyright 2010 DeepThought, Inc.<br />19<br />
  78. 78. Linear Regression and Model Statistics<br />M2 Example<br /><ul><li>F-Test
  79. 79. 22778.98
  80. 80. F-Test P-Value
  81. 81. 0.00 </li></ul>Copyright 2010 DeepThought, Inc.<br />20<br />
  82. 82. Linear Regression and Model Statistics<br />Compare Multiple Models<br /><ul><li>Skip this step until have knowledge of multiple methods
  83. 83. Will use accuracy/error statistics to compare multiple models to find best models</li></ul>Copyright 2010 DeepThought, Inc.<br />21<br />
  84. 84. Linear Regression and Model Statistics<br />Use Model<br /><ul><li>Understand limitations of model
  85. 85. Only measures a trend
  86. 86. A long term average
  87. 87. Answer objectives
  88. 88. Does M2 has a linear trend
  89. 89. If trend exists, what is its magnitude
  90. 90. If model statistically significant, forecast</li></ul>Copyright 2010 DeepThought, Inc.<br />22<br />
  91. 91. Linear Regression and Model Statistics<br />M2 Example<br /><ul><li>M2 = 1145.31 + 4.04 × Time
  92. 92. Next Period is 1519
  93. 93. Forecast for that period is:
  94. 94. Y = 1145.31 + 4.04 × 1519</li></ul>Y = 7283.446866 <br />Copyright 2010 DeepThought, Inc.<br />23<br />

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