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

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### 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 />