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

1. IBS Statistics Year 1 Dr. Ning DING n.ding@pl.hanze.nl I.007

3. Chapter 16:

4. Define the components of a time series

5. Compute a moving average

8. Chapter 16:

9. Define the components of a time series

10. Compute a moving average

11. Determine a linear trend equation98.87% SD increase Ŷ= -1.8182 + 0.1329X a

13. Ordinal:ranking

14. Interval:temperature, IQ

15. Ratio:age in years

17. Chapter 16:

18. Define the components of a time series

19. Compute a moving average

20. Determine a linear trend equationtrue zero Discrete counting or Continuous measuring

22. Chapter 16:

23. Define the components of a time series

24. Compute a moving average

25. Determine a linear trend equationQuantitative Data

27. Chapter 16:

28. Define the components of a time series

29. Compute a moving average

30. Determine a linear trend equation Classes f 10 up to 20 2 20 up to 30 1 30 up to 40 4 1 2 2 3 4 2 *15=30 1 *25=25 4 *35=140 10-<20 2 20 -<30 1 30-<40 4 Mean (1+2+2+3+4)/5 Mode Central Tendency 10-<20 2 20-<30 3 30-<40 7 L=(N+1)/2 (7+1)/2=4 Median

32. Chapter 16:

33. Define the components of a time series

34. Compute a moving average

35. Determine a linear trend equation10 up to 20 2 20 up to 30 1 30 up to 40 4 1 2 2 3 4 Range 4-1=3 Variance Dispersion Standard Deviation

37. Chapter 16:

38. Define the components of a time series

39. Compute a moving average

40. Determine a linear trend equationlarger than P42 Example Ch2 Mean =23.06

42. Chapter 16:

43. Define the components of a time series

44. Compute a moving average

45. Determine a linear trend equationStrong & Positive correlation Moderate & Positive correlation No correlation Moderate & Negative correlation Strong & Negative correlation Ŷ = a + bX

47. Chapter 16:

48. Define the components of a time series

49. Compute a moving average

50. Determine a linear trend equationY Axis: Dependent Variable Standard Error r2 = 1 r = -1 Standard Error = 0 7 6 5 4 3. 2 1 r2 = 0.24 r = -0.49 Standard Error = 2.5 Individual values are more scattered from the regression line. X Axis: Independent Variable 1 2 3 4 5 6 7

52. Chapter 16:

53. Define the components of a time series

54. Compute a moving average

56. Chapter 16:

57. Define the components of a time series

58. Compute a moving average

59. Determine a linear trend equationSample Exam P.4

61. Chapter 16:

62. Define the components of a time series

63. Compute a moving average

64. Determine a linear trend equationThe graph is positive. X There is a strong determination. X It is a srong positive correlation. X r =0.8619 so 86.19% of the variation in Y is explained by the variation in X. X r2=1.05 r = √ 1.05 = 1.025 = $1.025 X

66. Chapter 16:

67. Define the components of a time series

68. Compute a moving average

70. Chapter 16:

71. Define the components of a time series

72. Compute a moving average

74. Linear

75. Nonlinear

76. Cyclical variation

77. Rises and Falls over periods longer than one year

78. Seasonal variation

79. Patterns of change within a year, typically repeating themselves

80. Residual variationC S R

82. Chapter 16:

83. Define the components of a time series

84. Compute a moving average

86. Chapter 16:

87. Define the components of a time series

88. Compute a moving average

90. Chapter 16:

91. Define the components of a time series

92. Compute a moving average

94. Residual – also called chance fluctuation and unidentifiable

95. Review

96. Chapter 16:

97. Define the components of a time series

98. Compute a moving average

100. Basic method used in measuring seasonal fluctuation

101. Review

102. Chapter 16:

103. Define the components of a time series

104. Compute a moving average

106. Chapter 16:

107. Define the components of a time series

108. Compute a moving average

110. Chapter 16:

111. Define the components of a time series

112. Compute a moving average

114. Chapter 16:

115. Define the components of a time series

116. Compute a moving average

118. Chapter 16:

119. Define the components of a time series

120. Compute a moving average

122. Code time (t) and use it as the independent variable

123. E.g. let t be 1 for the first year, 2 for the second, and so on (if data are annual)

124. Review

125. Chapter 16:

126. Define the components of a time series

127. Compute a moving average

128. Determine a linear trend equationŶ = a + bX Ŷ = a + bt

130. E.g. let t be 1 for the first year, 2 for the second, and so on (if data are annual)

131. Review

132. Chapter 16:

133. Define the components of a time series

134. Compute a moving average

135. Determine a linear trend equationŶ = a + bt Example: The sales of Jensen Foods, a small grocery chain located in southwest Texas, since 2005 are: a = Y - bX

137. Chapter 16:

138. Define the components of a time series

139. Compute a moving average

140. Determine a linear trend equationa = Y - bX Step 5 = 1.3 Step 3 Ŷ = 6.1 + 1.3t a = 10 -1.3*3 = 6.1 Step 4

142. Chapter 16:

143. Define the components of a time series

144. Compute a moving average

145. Determine a linear trend equationŶ = 6.1 + 1.3t Example: The sales of Jensen Foods, a small grocery chain located in southwest Texas, since 2005 are:

147. Chapter 16:

148. Define the components of a time series

149. Compute a moving average

150. Determine a linear trend equationP152 N6 Ch16

152. Chapter 16:

153. Define the components of a time series

154. Compute a moving average

155. Determine a linear trend equationa = Y - bX P152 N6 Ch16

157. Chapter 16:

158. Define the components of a time series

159. Compute a moving average

160. Determine a linear trend equation 8 Ŷ 2007 9 = 1.73 a = 22.67 -1.73*4 = 15.75 Ŷ = 15.75 + 1.73*9 = $31.32 billions Ŷ = 15.75 + 1.73t P152 N6 Ch16

161. Hint Ŷ = a + bt Step 1 Code the year Step 2 Calculate X*Y, X2 a = Y - bX Step 3 Step 5 Formulate the least square equation What is the b? Ŷ = ? + ?*t Step 4 What is the a? P152 N6 Ch16

163. Chapter 16:

164. Define the components of a time series

165. Compute a moving average

166. Determine a linear trend equation