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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>