Lesson06

897 views

Published on

Statistics for International Business School, Hanze University of Applied Science, Groningen, The Netherlands

Published in: Technology, Education
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
897
On SlideShare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
44
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Lesson06

  1. 1. IBS Statistics<br />Year 1<br />Dr. Ning DING <br />n.ding@pl.hanze.nl<br />I.007<br />
  2. 2. What we are going to learn?<br /><ul><li>Review
  3. 3. Chapter 16:
  4. 4. Use a trend equation to forecast future time periods
  5. 5. Use a trend equation to developseasonallyadjustedforecasts
  6. 6. Determine and interpret a set of seasonal indexes
  7. 7. Desearsonalize data using a seasonal index</li></li></ul><li>Review<br /><ul><li>Review
  8. 8. Chapter 16:
  9. 9. Use a trend equation to forecast future time periods
  10. 10. Use a trend equation to developseasonallyadjustedforecasts
  11. 11. Determine and interpret a set of seasonal indexes
  12. 12. Desearsonalize data using a seasonal index</li></ul>Why Dispersion?<br />Central Tendency?<br />
  13. 13. Review<br />Dispersion<br /><ul><li>Review
  14. 14. Chapter 16:
  15. 15. Use a trend equation to forecast future time periods
  16. 16. Use a trend equation to developseasonallyadjustedforecasts
  17. 17. Determine and interpret a set of seasonal indexes
  18. 18. Desearsonalize data using a seasonal index</li></ul>Range Variance Standard Deviation<br />
  19. 19. Review<br />Dispersion<br /><ul><li>Review
  20. 20. Chapter 16:
  21. 21. Use a trend equation to forecast future time periods
  22. 22. Use a trend equation to developseasonallyadjustedforecasts
  23. 23. Determine and interpret a set of seasonal indexes
  24. 24. Desearsonalize data using a seasonal index</li></li></ul><li>Review<br />Don’tcompare the dispersion in data sets byusingtheir Standard Deviationsunlesstheirmeans are close to eachother. <br /><ul><li>Review
  25. 25. Chapter 16:
  26. 26. Use a trend equation to forecast future time periods
  27. 27. Use a trend equation to developseasonallyadjustedforecasts
  28. 28. Determine and interpret a set of seasonal indexes
  29. 29. Desearsonalize data using a seasonal index</li></ul>Whichone has more variation in the data?<br />Example :<br />20 poundsoverweight<br />Mean=120 pounds<br />Mean=170 pounds<br />CV=20/120 =16.7%<br />CV=20/170 =12.5%<br />Coefficient of Variation (CV)= Standard Deviation / Mean<br />
  30. 30. Review<br />2<br />3<br />4<br />5<br />6<br />7<br />10<br />13<br />2<br />3<br />4<br />4.25<br />4.75<br />7<br />8<br />9<br />2<br />3<br />4<br />5<br />6<br />7<br />8<br />9<br />2<br />3<br />3.25<br />3.50<br />3.75<br />4<br />5<br />9<br />Median= 5.5 5.5 4.5 3.38<br /><ul><li>Review
  31. 31. Chapter 16:
  32. 32. Use a trend equation to forecast future time periods
  33. 33. Use a trend equation to developseasonallyadjustedforecasts
  34. 34. Determine and interpret a set of seasonal indexes
  35. 35. Desearsonalize data using a seasonal index</li></ul>Mean= 5.5 6.25 5.25 4.19<br />
  36. 36. Review<br />Most skewed?<br /><ul><li>Review
  37. 37. Chapter 16:
  38. 38. Use a trend equation to forecast future time periods
  39. 39. Use a trend equation to developseasonallyadjustedforecasts
  40. 40. Determine and interpret a set of seasonal indexes
  41. 41. Desearsonalize data using a seasonal index</li></ul>Median= 5.5 5.5 4.5 3.38<br />Mean= 5.5 6.25 5.25 4.19<br />
  42. 42. Review<br />Positive Correlation<br /><ul><li>Review
  43. 43. Chapter 16:
  44. 44. Use a trend equation to forecast future time periods
  45. 45. Use a trend equation to developseasonallyadjustedforecasts
  46. 46. Determine and interpret a set of seasonal indexes
  47. 47. Desearsonalize data using a seasonal index</li></ul>Negative Correlation<br />
  48. 48. Review<br /><ul><li>Review
  49. 49. Chapter 16:
  50. 50. Use a trend equation to forecast future time periods
  51. 51. Use a trend equation to developseasonallyadjustedforecasts
  52. 52. Determine and interpret a set of seasonal indexes
  53. 53. Desearsonalize data using a seasonal index</li></ul>Secular trend<br />Seasonalvariation<br />Sales<br />Q4<br />Q2<br />Q3<br />Cyclicalfluctuation<br />Q1<br />Irregularvariation<br />2001 2002 2003 2004 2005 2006 2007 2008 2009 2010<br />Years<br />
  54. 54. Review<br />Applicable when time series follows fairly linear trendthat have definite rhythmic pattern<br /><ul><li>Review
  55. 55. Chapter 16:
  56. 56. Use a trend equation to forecast future time periods
  57. 57. Use a trend equation to developseasonallyadjustedforecasts
  58. 58. Determine and interpret a set of seasonal indexes
  59. 59. Desearsonalize data using a seasonal index</li></li></ul><li>Seven-Year Moving Total<br />Moving Average<br />1+2+3+4+5+4+3=22<br />/ 7 = 3.143<br /><ul><li>Review
  60. 60. Chapter 16:
  61. 61. Use a trend equation to forecast future time periods
  62. 62. Use a trend equation to developseasonallyadjustedforecasts
  63. 63. Determine and interpret a set of seasonal indexes
  64. 64. Desearsonalize data using a seasonal index</li></ul>2+3+4+5+4+3+2=23<br />/ 7 = 3.286<br />3+4+5+4+3+2+3=24<br />/ 7 = 3.429<br />SevenYearMoving Average<br />
  65. 65. Ŷ = a + bt<br />Review<br /><ul><li>Review
  66. 66. Chapter 16:
  67. 67. Use a trend equation to forecast future time periods
  68. 68. Use a trend equation to developseasonallyadjustedforecasts
  69. 69. Determine and interpret a set of seasonal indexes
  70. 70. Desearsonalize data using a seasonal index</li></ul>= 1.73<br />a = 22.67 -1.73*4 = 15.75<br />a = Y - bX<br />P152 N6 Ch16<br />
  71. 71. Ŷ = a + bt<br />Review<br />= 1.73<br /><ul><li>Review
  72. 72. Chapter 16:
  73. 73. Use a trend equation to forecast future time periods
  74. 74. Use a trend equation to developseasonallyadjustedforecasts
  75. 75. Determine and interpret a set of seasonal indexes
  76. 76. Desearsonalize data using a seasonal index</li></ul>a = 22.67 = 22.67<br />a = Y - bX<br />a = Y<br />Ŷ = 22.67 + 1.73t<br />
  77. 77. Ŷ = a + bt<br />Review<br /><ul><li>Review
  78. 78. Chapter 16:
  79. 79. Use a trend equation to forecast future time periods
  80. 80. Use a trend equation to developseasonallyadjustedforecasts
  81. 81. Determine and interpret a set of seasonal indexes
  82. 82. Desearsonalize data using a seasonal index</li></ul>a = Y<br />Odd-numbered<br />Even-numbered<br />
  83. 83. Seasonal Variation<br />Understanding seasonal fluctuationshelp plan for sufficient goods and materials on hand to meet varying seasonal demand<br /><ul><li>Review
  84. 84. Chapter 16:
  85. 85. Use a trend equation to forecast future time periods
  86. 86. Use a trend equation to developseasonallyadjustedforecasts
  87. 87. Determine and interpret a set of seasonal indexes
  88. 88. Desearsonalize data using a seasonal index</li></li></ul><li>Seasonal Variation<br />Seasonal variations are fluctuations that coincide with certain seasons and are repeated year after year<br /><ul><li>Review
  89. 89. Chapter 16:
  90. 90. Use a trend equation to forecast future time periods
  91. 91. Use a trend equation to developseasonallyadjustedforecasts
  92. 92. Determine and interpret a set of seasonal indexes
  93. 93. Desearsonalize data using a seasonal index</li></li></ul><li>Seasonal Variation<br />Seasonal Index:<br />A number, usually expressed in percent, that expresses the relative valueof a season with respect to the average for the year(100%)<br /><ul><li>Review
  94. 94. Chapter 16:
  95. 95. Use a trend equation to forecast future time periods
  96. 96. Use a trend equation to developseasonallyadjustedforecasts
  97. 97. Determine and interpret a set of seasonal indexes
  98. 98. Desearsonalize data using a seasonal index</li></ul>SalesforJuly are 14% belowan average month. <br />Sales for December are 26.8% above an average month. <br />
  99. 99. Seasonal Variation<br /><ul><li>Review
  100. 100. Chapter 16:
  101. 101. Use a trend equation to forecast future time periods
  102. 102. Use a trend equation to developseasonallyadjustedforecasts
  103. 103. Determine and interpret a set of seasonal indexes
  104. 104. Desearsonalize data using a seasonal index</li></ul>Sales Report: in $ millions<br />2005<br />2006<br />2007<br />2008<br />2009<br />2010<br />
  105. 105. Seasonal Variation<br /><ul><li>Review
  106. 106. Chapter 16:
  107. 107. Use a trend equation to forecast future time periods
  108. 108. Use a trend equation to developseasonallyadjustedforecasts
  109. 109. Determine and interpret a set of seasonal indexes
  110. 110. Desearsonalize data using a seasonal index</li></ul>Step 1: Re-organize the data<br />2005<br />2006<br />2007<br />2008<br />2009<br />2010<br />
  111. 111. Seasonal Variation<br /><ul><li>Review
  112. 112. Chapter 16:
  113. 113. Use a trend equation to forecast future time periods
  114. 114. Use a trend equation to developseasonallyadjustedforecasts
  115. 115. Determine and interpret a set of seasonal indexes
  116. 116. Desearsonalize data using a seasonal index</li></ul>6.7+4.6+10.0+12.7=34<br />/4=8.50<br />4.6+10.0+12.7+6.5=33.8<br />/4=8.45<br />Step 2: Moving Average<br />
  117. 117. Seasonal Variation<br /><ul><li>Review
  118. 118. Chapter 16:
  119. 119. Use a trend equation to forecast future time periods
  120. 120. Use a trend equation to developseasonallyadjustedforecasts
  121. 121. Determine and interpret a set of seasonal indexes
  122. 122. Desearsonalize data using a seasonal index</li></ul>Step 3: Centered Moving Average<br />
  123. 123. Seasonal Variation<br /><ul><li>Review
  124. 124. Chapter 16:
  125. 125. Use a trend equation to forecast future time periods
  126. 126. Use a trend equation to developseasonallyadjustedforecasts
  127. 127. Determine and interpret a set of seasonal indexes
  128. 128. Desearsonalize data using a seasonal index</li></ul>Step 4: SpecificSeasonal Index<br />
  129. 129. Seasonal Variation<br /><ul><li>Review
  130. 130. Chapter 16:
  131. 131. Use a trend equation to forecast future time periods
  132. 132. Use a trend equation to developseasonallyadjustedforecasts
  133. 133. Determine and interpret a set of seasonal indexes
  134. 134. Desearsonalize data using a seasonal index</li></ul>10/8.475=1.180<br />12.7/8.45=1.503<br />6.5/8.425=0.772<br />Step 4: Specific Seasonal Index<br />
  135. 135. Seasonal Variation<br />2005<br />2006<br />2007<br />2008<br />2009<br />2010<br /><ul><li>Review
  136. 136. Chapter 16:
  137. 137. Use a trend equation to forecast future time periods
  138. 138. Use a trend equation to developseasonallyadjustedforecasts
  139. 139. Determine and interpret a set of seasonal indexes
  140. 140. Desearsonalize data using a seasonal index</li></ul>+ + + =<br />*(0.9978)<br />*(0.9978)<br />*(0.9978)<br />*(0.9978)<br />Step 5: TypicalQuarterly Index<br />
  141. 141. Seasonal Variation<br />Sales for the Winter are 23.5% below the typical quarter.<br />2005<br />2006<br />2007<br />2008<br />2009<br />2010<br /><ul><li>Review
  142. 142. Chapter 16:
  143. 143. Use a trend equation to forecast future time periods
  144. 144. Use a trend equation to developseasonallyadjustedforecasts
  145. 145. Determine and interpret a set of seasonal indexes
  146. 146. Desearsonalize data using a seasonal index</li></ul>Salesfor the Fall are 51.9% above the typicalquarter. <br />Step 6: Interpret<br />
  147. 147. Exercise<br />Appliance Center sells a variety of electronic equipment and home appliances. For the last four years the following quarterly sales (in $ millions) were reported.<br />Determine a typical seasonal index for each of the four quarters. <br /><ul><li>Review
  148. 148. Chapter 16:
  149. 149. Use a trend equation to forecast future time periods
  150. 150. Use a trend equation to developseasonallyadjustedforecasts
  151. 151. Determine and interpret a set of seasonal indexes
  152. 152. Desearsonalize data using a seasonal index</li></ul>P161 No.10 Ch16<br />
  153. 153. Exercise<br />Step 1: Reorganize the data<br /><ul><li>Review
  154. 154. Chapter 16:
  155. 155. Use a trend equation to forecast future time periods
  156. 156. Use a trend equation to developseasonallyadjustedforecasts
  157. 157. Determine and interpret a set of seasonal indexes
  158. 158. Desearsonalize data using a seasonal index</li></ul>Step 2: Moving Average<br />Step 3: Centered Moving Average<br />Step 4: Specific Seasonal Index<br />P161 No.10 Ch16<br />
  159. 159. Step 5: Reorganize the data<br /><ul><li>Review
  160. 160. Chapter 16:
  161. 161. Use a trend equation to forecast future time periods
  162. 162. Use a trend equation to developseasonallyadjustedforecasts
  163. 163. Determine and interpret a set of seasonal indexes
  164. 164. Desearsonalize data using a seasonal index</li></ul>Step 6: Calculate the mean for each quarter<br />Step 8: Divide 4 by Total of four means to get Correction Factor<br />Step 7: Sum up the four means<br />Step 9: Mean * Correction Factor<br />P161 No.10 Ch16<br />
  165. 165. DeseasonalizingData<br /><ul><li>Review
  166. 166. Chapter 16:
  167. 167. Use a trend equation to forecast future time periods
  168. 168. Use a trend equation to develop seasonally adjusted forecasts
  169. 169. Determine and interpret a set of seasonal indexes
  170. 170. Desearsonalize data using a seasonal index</li></ul>To remove the seasonal fluctuations so that the trend and cycle can be studied.<br />Ŷ = a + bt<br />Ŷ = a + bX<br />
  171. 171. 76.5<br />57.5<br />114.1<br />151.9<br /><ul><li>Review
  172. 172. Chapter 16:
  173. 173. Use a trend equation to forecast future time periods
  174. 174. Use a trend equation to developseasonallyadjustedforecasts
  175. 175. Determine and interpret a set of seasonal indexes
  176. 176. Desearsonalize data using a seasonal index</li></ul>/ 0.765<br />= 8.759<br />/ 0.575<br />= 8.004<br />/ 1.141<br />= 8.761<br />/ 1.519<br />= 8.361<br />/ 0.765<br />/ 0.575<br />/ 1.141<br />/ 1.519<br />/ 0.765<br />/ 0.575<br />/ 1.141<br />= 8.498<br />= 9.021<br />/ 1.519<br />= 8.004<br />= 8.700<br />= 8.586<br />= 9.112<br />= 8.953<br />= 9.283<br />
  177. 177. DeseasonalizingData<br />Ŷ = a + bt<br />Chapter 16: Time Series & Forecasting<br />76.5<br />57.5<br />114.1<br />151.9<br /><ul><li>Review
  178. 178. Chapter 16:
  179. 179. Use a trend equation to forecast future time periods
  180. 180. Use a trend equation to developseasonallyadjustedforecasts
  181. 181. Determine and interpret a set of seasonal indexes
  182. 182. Desearsonalize data using a seasonal index</li></ul>Ŷ = 8.1096 + 0.0899 t<br />Sale increased at a rate of 0.0899 ($ millions) per quarter.<br />Ŷ = 8.1096 + 0.0899 * 25<br />= 10.3571 $ millions<br />10.3571*0.765 = 7.9232 $ millions<br />
  183. 183. Home Assignment<br /><ul><li>Review
  184. 184. Chapter 16:
  185. 185. Use a trend equation to forecast future time periods
  186. 186. Use a trend equation to develop seasonally adjusted forecasts
  187. 187. Determine and interpret a set of seasonal indexes
  188. 188. Desearsonalize data using a seasonal index</li></ul>1. Calculate the seasonal indices for each quarter, express them as a ratio and not as a %. You may round to 4 dec. places. <br />Wed, 06, 12:00 a.m. 2011<br />Pigeon hole Ning Ding<br />2. Interpret the seasonal index quarter II. <br />3. Deseasonalized the original revenue for 2008 quarter I.<br />4. For 2011 quarter II the forecasted revenue from the trend line was 55. Calculate the seasonalized revenue for 2011 quarter II. <br />
  189. 189. What we have learnt?<br /><ul><li>Review
  190. 190. Chapter 16:
  191. 191. Use a trend equation to forecast future time periods
  192. 192. Use a trend equation to developseasonallyadjustedforecasts
  193. 193. Determine and interpret a set of seasonal indexes
  194. 194. Desearsonalize data using a seasonal index</li></li></ul><li>Step 7: Sum up the four means<br />Step 1: Reorganize the data<br />Step 8: Divide 4 by Total of four means to get Correction Factor<br />Step 2: Moving Average<br />Step 3: Centered Moving Average<br />Step 9: Mean * Correction Factor<br />Step 4: Specific Seasonal Index<br />Step 5: Reorganize the data<br />Step 6: Calculate the mean for each quarter<br />Hint<br />

×