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IBS Statistics<br />Year 1<br />Dr. Ning DING <br />n.ding@pl.hanze.nl<br />I.007<br />
What we are going to learn?<br /><ul><li>Review
Chapter 16:
Define the components of a time series
Compute a moving average
Determine a linear trend equation</li></li></ul><li>Chapter 12: Sim Reg & Corr<br />Exercise<br />Ŷ= -1.8182 + 0.1329X<br ...
r2<br /><ul><li>Review
Chapter 16:
Define the components of a time series
Compute a moving average
Determine a linear trend equation</li></ul>98.87%<br />SD<br />increase<br />Ŷ= -1.8182 + 0.1329X<br />a<br />
Review Chapter 1<br /><ul><li>Nominal: gender
Ordinal:ranking
Interval:temperature, IQ
Ratio:age in years
Qualitative: </li></ul>gender, eye color, <br /><ul><li>Quantitative:</li></ul>income, distance<br /><ul><li>Review
Chapter 16:
Define the components of a time series
Compute a moving average
Determine a linear trend equation</li></ul>true zero<br />Discrete counting            or         Continuous measuring<b...
Review Chapter 2<br />Pie Chart<br />Bar Chart<br />Cumulative Frequency<br />Distribution<br />Histogram<br />Polygon<br ...
Chapter 16:
Define the components of a time series
Compute a moving average
Determine a linear trend equation</li></ul>Quantitative Data<br />
Review Chapter 3<br />195<br />7<br />=24.86<br />40<br />32.5<br />30<br />3<br />7<br />4<br />5<br />6<br />Ungrouped D...
Chapter 16:
Define the components of a time series
Compute a moving average
Determine a linear trend equation</li></ul>     Classes      f  <br />10 up to 20    2<br />20 up to 30    1<br />30 up to...
Review Chapter 3<br />195<br />7<br />=24.86<br />Grouped Data<br />Ungrouped Data<br /><ul><li>Review
Chapter 16:
Define the components of a time series
Compute a moving average
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Lesson05

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

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Lesson05

  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. Define the components of a time series
  5. 5. Compute a moving average
  6. 6. Determine a linear trend equation</li></li></ul><li>Chapter 12: Sim Reg & Corr<br />Exercise<br />Ŷ= -1.8182 + 0.1329X<br />Sample Exam P.4<br />
  7. 7. r2<br /><ul><li>Review
  8. 8. Chapter 16:
  9. 9. Define the components of a time series
  10. 10. Compute a moving average
  11. 11. Determine a linear trend equation</li></ul>98.87%<br />SD<br />increase<br />Ŷ= -1.8182 + 0.1329X<br />a<br />
  12. 12. Review Chapter 1<br /><ul><li>Nominal: gender
  13. 13. Ordinal:ranking
  14. 14. Interval:temperature, IQ
  15. 15. Ratio:age in years
  16. 16. Qualitative: </li></ul>gender, eye color, <br /><ul><li>Quantitative:</li></ul>income, distance<br /><ul><li>Review
  17. 17. Chapter 16:
  18. 18. Define the components of a time series
  19. 19. Compute a moving average
  20. 20. Determine a linear trend equation</li></ul>true zero<br />Discrete counting or Continuous measuring<br />
  21. 21. Review Chapter 2<br />Pie Chart<br />Bar Chart<br />Cumulative Frequency<br />Distribution<br />Histogram<br />Polygon<br />Qualitative Data<br /><ul><li>Review
  22. 22. Chapter 16:
  23. 23. Define the components of a time series
  24. 24. Compute a moving average
  25. 25. Determine a linear trend equation</li></ul>Quantitative Data<br />
  26. 26. Review Chapter 3<br />195<br />7<br />=24.86<br />40<br />32.5<br />30<br />3<br />7<br />4<br />5<br />6<br />Ungrouped Data<br />Grouped Data<br /><ul><li>Review
  27. 27. Chapter 16:
  28. 28. Define the components of a time series
  29. 29. Compute a moving average
  30. 30. Determine a linear trend equation</li></ul> Classes f <br />10 up to 20 2<br />20 up to 30 1<br />30 up to 40 4<br />1 2 2 3 4<br />2 *15=30<br />1 *25=25<br />4 *35=140<br />10-<20 2<br />20 -<30 1<br />30-<40 4<br />Mean<br />(1+2+2+3+4)/5<br />Mode<br />Central Tendency<br />10-<20 2<br />20-<30 3<br />30-<40 7<br />L=(N+1)/2<br />(7+1)/2=4<br />Median<br />
  31. 31. Review Chapter 3<br />195<br />7<br />=24.86<br />Grouped Data<br />Ungrouped Data<br /><ul><li>Review
  32. 32. Chapter 16:
  33. 33. Define the components of a time series
  34. 34. Compute a moving average
  35. 35. Determine a linear trend equation</li></ul>10 up to 20 2<br />20 up to 30 1<br />30 up to 40 4<br />1 2 2 3 4<br />Range<br />4-1=3<br />Variance<br />Dispersion<br />Standard Deviation<br />
  36. 36. Review Chapter 4<br />Interquartile Range<br />The distribution is skewed to __________<br />because the mean is __________the median. <br />the right <br /><ul><li>Review
  37. 37. Chapter 16:
  38. 38. Define the components of a time series
  39. 39. Compute a moving average
  40. 40. Determine a linear trend equation</li></ul>larger than<br />P42 Example Ch2<br />Mean =23.06<br />
  41. 41. ReviewChapter 12<br />r = 0.9<br />r = -0.9<br />r = 0.6<br />r = -0.6<br />r = 0<br /><ul><li>Review
  42. 42. Chapter 16:
  43. 43. Define the components of a time series
  44. 44. Compute a moving average
  45. 45. Determine a linear trend equation</li></ul>Strong & Positive<br />correlation<br />Moderate & Positive<br />correlation<br />No<br />correlation<br />Moderate & Negative<br />correlation<br />Strong & Negative<br />correlation<br />Ŷ = a + bX<br />
  46. 46. ReviewChapter 12<br />Standard Error<br />Ŷ = a + bX<br /><ul><li>Review
  47. 47. Chapter 16:
  48. 48. Define the components of a time series
  49. 49. Compute a moving average
  50. 50. Determine a linear trend equation</li></ul>Y Axis: Dependent Variable<br />Standard Error<br />r2 = 1 r = -1<br />Standard Error = 0<br />7<br />6<br />5<br />4<br />3.<br />2<br />1<br />r2 = 0.24 r = -0.49<br />Standard Error = 2.5<br />Individual values are more scattered from the regression line. <br />X Axis: <br />Independent Variable<br />1 2 3 4 5 6 7<br />
  51. 51. ReviewChapter 12<br />Least Square Regression Equation<br />Ŷ = a + bX<br /><ul><li>Review
  52. 52. Chapter 16:
  53. 53. Define the components of a time series
  54. 54. Compute a moving average
  55. 55. Determine a linear trend equation</li></li></ul><li>Ŷ= -1.8182 + 0.1329X<br /><ul><li>Review
  56. 56. Chapter 16:
  57. 57. Define the components of a time series
  58. 58. Compute a moving average
  59. 59. Determine a linear trend equation</li></ul>Sample Exam P.4<br />
  60. 60. ReviewChapter 12<br /><ul><li>Review
  61. 61. Chapter 16:
  62. 62. Define the components of a time series
  63. 63. Compute a moving average
  64. 64. Determine a linear trend equation</li></ul>The graph is positive.<br />X<br />There is a strong determination.<br />X<br />It is a srong positive correlation.<br />X<br />r =0.8619 so 86.19% of the variation in Y is explained by the variation in X. <br />X<br />r2=1.05 r = √ 1.05 = 1.025 = $1.025<br />X<br />
  65. 65. Chapter 16: <br />Time Series & Forecasting<br /><ul><li>Review
  66. 66. Chapter 16:
  67. 67. Define the components of a time series
  68. 68. Compute a moving average
  69. 69. Determine a linear trend equation</li></li></ul><li>Components of a Time Series<br />Time series:<br />a collection of data recorded over a period of time (weekly, monthly, quarterly), an analysis of history, that can be used by management to make current decisions and plans based on long-term forecasting. <br /><ul><li>Review
  70. 70. Chapter 16:
  71. 71. Define the components of a time series
  72. 72. Compute a moving average
  73. 73. Determine a linear trend equation</li></ul>S<br /><ul><li>Secular Trend
  74. 74. Linear
  75. 75. Nonlinear
  76. 76. Cyclical variation
  77. 77. Rises and Falls over periods longer than one year
  78. 78. Seasonal variation
  79. 79. Patterns of change within a year, typically repeating themselves
  80. 80. Residual variation</li></ul>C<br />S<br />R<br />
  81. 81. Components of a Time Series<br />Secular Trend:<br />The smooth long-term direction of a time series. <br /><ul><li>Review
  82. 82. Chapter 16:
  83. 83. Define the components of a time series
  84. 84. Compute a moving average
  85. 85. Determine a linear trend equation</li></li></ul><li>Cyclical Variation:<br />The rise and fall of a time series over periods longer than one year. <br /><ul><li>Review
  86. 86. Chapter 16:
  87. 87. Define the components of a time series
  88. 88. Compute a moving average
  89. 89. Determine a linear trend equation</li></li></ul><li>Seasonal Variation:<br />Patterns of change in a time series within a year. These patterns tend to repeat themselves each year. <br /><ul><li>Review
  90. 90. Chapter 16:
  91. 91. Define the components of a time series
  92. 92. Compute a moving average
  93. 93. Determine a linear trend equation</li></li></ul><li>Irregular Variation:<br /><ul><li> Episodic – unpredictable but identifiable
  94. 94. Residual – also called chance fluctuation and unidentifiable
  95. 95. Review
  96. 96. Chapter 16:
  97. 97. Define the components of a time series
  98. 98. Compute a moving average
  99. 99. Determine a linear trend equation</li></li></ul><li>Moving Average:<br /><ul><li>Useful in smoothing time series to see its trend
  100. 100. Basic method used in measuring seasonal fluctuation
  101. 101. Review
  102. 102. Chapter 16:
  103. 103. Define the components of a time series
  104. 104. Compute a moving average
  105. 105. Determine a linear trend equation</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 />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 /><ul><li>Review
  106. 106. Chapter 16:
  107. 107. Define the components of a time series
  108. 108. Compute a moving average
  109. 109. Determine a linear trend equation</li></li></ul><li>Moving Average:<br /><ul><li>Review
  110. 110. Chapter 16:
  111. 111. Define the components of a time series
  112. 112. Compute a moving average
  113. 113. Determine a linear trend equation</li></li></ul><li><ul><li>Review
  114. 114. Chapter 16:
  115. 115. Define the components of a time series
  116. 116. Compute a moving average
  117. 117. Determine a linear trend equation</li></li></ul><li>Linear Trend<br />The long term trend of many business series often approximates a straight line<br /><ul><li>Review
  118. 118. Chapter 16:
  119. 119. Define the components of a time series
  120. 120. Compute a moving average
  121. 121. Determine a linear trend equation</li></li></ul><li>Linear Trend<br /><ul><li>Use the least squares method in Simple Linear Regression (Chapter 12) to find the best linear relationship between 2 variables
  122. 122. Code time (t) and use it as the independent variable
  123. 123. E.g. let t be 1 for the first year, 2 for the second, and so on (if data are annual)
  124. 124. Review
  125. 125. Chapter 16:
  126. 126. Define the components of a time series
  127. 127. Compute a moving average
  128. 128. Determine a linear trend equation</li></ul>Ŷ = a + bX<br />Ŷ = a + bt<br />
  129. 129. Linear Trend<br /><ul><li>Code time (t) and use it as the independent variable
  130. 130. E.g. let t be 1 for the first year, 2 for the second, and so on (if data are annual)
  131. 131. Review
  132. 132. Chapter 16:
  133. 133. Define the components of a time series
  134. 134. Compute a moving average
  135. 135. Determine a linear trend equation</li></ul>Ŷ = a + bt<br />Example:<br />The sales of Jensen Foods, a small grocery chain located in southwest Texas, since 2005 are:<br />a = Y - bX<br />
  136. 136. Linear Trend<br />Ŷ = a + bt<br />Step 1<br />Step 2<br /><ul><li>Review
  137. 137. Chapter 16:
  138. 138. Define the components of a time series
  139. 139. Compute a moving average
  140. 140. Determine a linear trend equation</li></ul>a = Y - bX<br />Step 5<br />= 1.3<br />Step 3<br />Ŷ = 6.1 + 1.3t<br />a = 10 -1.3*3 = 6.1<br />Step 4<br />
  141. 141. Linear Trend<br />Ŷ = 6.1 + 1.3*7 = 15.2<br />? 2011 ?<br />$ millions<br /><ul><li>Review
  142. 142. Chapter 16:
  143. 143. Define the components of a time series
  144. 144. Compute a moving average
  145. 145. Determine a linear trend equation</li></ul>Ŷ = 6.1 + 1.3t<br />Example:<br />The sales of Jensen Foods, a small grocery chain located in southwest Texas, since 2005 are:<br />
  146. 146. Exercise<br />The amounts spent in vending machines in the United States, in billions of dollars, for the years 1999 through 2005 are given below. Determine the least-squares trend equation and estimate vending sales for 2007. <br /><ul><li>Review
  147. 147. Chapter 16:
  148. 148. Define the components of a time series
  149. 149. Compute a moving average
  150. 150. Determine a linear trend equation</li></ul>P152 N6 Ch16<br />
  151. 151. Exercise<br />= 1.73<br />Ŷ = a + bt<br />a = 22.67 -1.73*4 = 15.75<br /><ul><li>Review
  152. 152. Chapter 16:
  153. 153. Define the components of a time series
  154. 154. Compute a moving average
  155. 155. Determine a linear trend equation</li></ul>a = Y - bX<br />P152 N6 Ch16<br />
  156. 156. Exercise<br /><ul><li>Review
  157. 157. Chapter 16:
  158. 158. Define the components of a time series
  159. 159. Compute a moving average
  160. 160. Determine a linear trend equation</li></ul> 8 Ŷ<br />2007 9<br />= 1.73<br />a = 22.67 -1.73*4 = 15.75<br />Ŷ = 15.75 + 1.73*9 = $31.32 billions <br />Ŷ = 15.75 + 1.73t<br />P152 N6 Ch16<br />
  161. 161. Hint<br />Ŷ = a + bt<br />Step 1<br />Code the year<br />Step 2<br />Calculate X*Y, X2<br />a = Y - bX<br />Step 3<br />Step 5<br />Formulate the least square equation<br />What is the b?<br />Ŷ = ? + ?*t<br />Step 4<br />What is the a?<br />P152 N6 Ch16<br />
  162. 162. What we have learnt?<br /><ul><li>Review
  163. 163. Chapter 16:
  164. 164. Define the components of a time series
  165. 165. Compute a moving average
  166. 166. Determine a linear trend equation</li>

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