Lesson05

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

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  • More explanation: http://www.ncsu.edu/labwrite/res/gt/gt-reg-home.html
  • 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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