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# Lesson04

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

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### Lesson04

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. Chapter12: Simple Regression and Correlation
4. 4. dependent / independent variables
5. 5. scatterdiagrams
6. 6. regressionanalysis
7. 7. Least-squares estimatingequation
8. 8. the coefficient of determination
9. 9. the coefficient of correlation</li></li></ul><li>Review<br /><ul><li>Review
10. 10. Chapter12: Simple Regression and Correlation
11. 11. Exercises</li></ul>Find the interquartile range:<br /> <br />1460<br />1471<br />1637<br />1721<br />1758<br />1787 <br />1940<br />2038<br />2047<br />2054 <br />2097<br />2205<br />2287<br />2311<br />2406<br />Interquartile Range<br />=Q3-Q1<br />=2205-1721<br />=484<br />
12. 12. Review EXCEL Lesson<br /><ul><li>Review
13. 13. Chapter12: Simple Regression and Correlation
14. 14. Exercises</li></ul>L=(8+1)*25%=2.25<br />Q1=133.5<br />Interquartile Range<br />=274.5-133.5<br />=141<br />L=(8+1)*75%=6.75<br />Q3=274.5<br />
15. 15. Review<br />Median<br />Quartile<br />Decile<br />Percentile<br />1<br />2<br />2<br />4<br />1<br />2<br />2<br />4<br />5<br />7<br />8<br />9<br />12<br />1st D<br />Q1=2<br />Interquartile<br />Range<br />5<br />7<br />8<br />9<br />12<br />Q3=8.5<br />9th D<br />Boxplot<br />How to interpret?<br />http://cnx.org/content/m11192/latest/<br />
16. 16. Review<br /><ul><li>Review
17. 17. Chapter12: Simple Regression and Correlation
18. 18. Exercises</li></ul>Mean= € 450<br />a<br />b<br />€ 20<br />€ 2000<br />Q1= € 250<br />Q3= € 850<br />Median= € 350<br />The distribution is skewed to __________ because the mean is __________the median. <br />the right <br />larger than <br />http://cnx.org/content/m11192/latest/<br />
19. 19. 0.8<br />1.0<br />1.0<br />1.2<br />1.2<br />1.3<br />1.5<br />1.7<br />2.0<br />2.0<br />2.1<br />2.2<br />4.0<br />Review<br />Mean > Median<br />2.0<br />3.2<br />3.6<br />3.7<br />4.0<br />4.2<br />4.2<br />4.5<br />4.5<br />4.6<br />4.8<br />5.0<br />5.0<br />Mean < Median<br />Positively skewed<br />http://qudata.com/online/statcalc/<br />Negatively skewed<br />
20. 20. Review<br />This means that the data is symmetrically distributed. <br />Zero skewness<br />mode=median=mean<br />
21. 21. Chapter 12<br /><ul><li>Review
22. 22. Chapter12:
23. 23. scatterdiagrams
24. 24. dependent / independent variables
25. 25. regressionanalysis
26. 26. Least-squares estimatingequation
27. 27. the coefficient of determination
28. 28. the coefficient of correlation
29. 29. scatterdiagrams
30. 30. dependent / independent variables
31. 31. regressionanalysis
32. 32. Least-squares estimatingequation
33. 33. the coefficient of determination
34. 34. the coefficient of correlation</li></li></ul><li>Regression and Correlation Analyses<br /><ul><li>Review
35. 35. Chapter12:
36. 36. scatter diagrams
37. 37. dependent / independent variables
38. 38. regressionanalysis
39. 39. Least-squares estimatingequation
40. 40. the coefficient of determination
41. 41. the coefficient of correlation
42. 42. How to determine both the nature and the strength of a relationship between variables. </li></li></ul><li>Regression and Correlation Analyses<br /><ul><li>Review
43. 43. Chapter12:
44. 44. scatterdiagrams
45. 45. dependent / independent variables
46. 46. regressionanalysis
47. 47. Least-squares estimatingequation
48. 48. the coefficient of determination
49. 49. the coefficient of correlation</li></ul>Scatter Diagram:<br />Positive correlation<br />
50. 50. Regression and Correlation Analyses<br /><ul><li>Review
51. 51. Chapter12:
52. 52. scatterdiagrams
53. 53. dependent / independent variables
54. 54. regressionanalysis
55. 55. Least-squares estimatingequation
56. 56. the coefficient of determination
57. 57. the coefficient of correlation</li></ul>Scatter Diagram:<br />Negative correlation<br />
58. 58. Regression and Correlation Analyses<br /><ul><li>Review
59. 59. Chapter12:
60. 60. scatterdiagrams
61. 61. dependent / independent variables
62. 62. regressionanalysis
63. 63. Least-squares estimatingequation
64. 64. the coefficient of determination
65. 65. the coefficient of correlation</li></ul>Scatter Diagram:<br />No correlation<br />
66. 66. Regression and Correlation Analyses<br /><ul><li>Review
67. 67. Chapter12:
68. 68. scatterdiagrams
69. 69. dependent / independent variables
70. 70. regressionanalysis
71. 71. Least-squares estimatingequation
72. 72. the coefficient of determination
73. 73. the coefficient of correlation</li></ul>Scatter Diagrams:<br /><ul><li>Patterns indicating that the variables are related
74. 74. If related, we can describe the relationship</li></ul>Weak & Positive<br />correlation<br />Strong & Positive<br />correlation<br />No<br />correlation<br />Weak & Negative<br />correlation<br />Strong & Negative<br />correlation<br />
75. 75. Regression and Correlation Analyses<br /><ul><li>Review
76. 76. Chapter12:
77. 77. scatterdiagrams
78. 78. dependent / independent variables
79. 79. regressionanalysis
80. 80. Least-squares estimatingequation
81. 81. the coefficient of determination
82. 82. the coefficient of correlation
83. 83. Independent variables: known
84. 84. Dependent variables: to predict</li></ul>Variables: <br />DependentVariable<br />Independent Variable<br />
85. 85. Regression and Correlation Analyses<br /><ul><li>Review
86. 86. Chapter12:
87. 87. scatterdiagrams
88. 88. dependent / independent variables
89. 89. regressionanalysis
90. 90. Least-squares estimatingequation
91. 91. the coefficient of determination
92. 92. the coefficient of correlation</li></ul>Correlation & Cause Effect?<br /><ul><li>The relationships found by regression to be relationships of association
93. 93. Notnecessarilly of cause and effect.</li></li></ul><li><ul><li>Review
94. 94. Chapter12:
95. 95. scatterdiagrams
96. 96. dependent / independent variables
97. 97. regressionanalysis
98. 98. Least-squares estimatingequation
99. 99. the coefficient of determination
100. 100. the coefficient of correlation</li></li></ul><li>Least-squares estimating equation:<br /><ul><li>The dependent variable Y is determined by the independent variable X</li></ul>Y<br /> X<br /><ul><li>Review
101. 101. Chapter12:
102. 102. scatterdiagrams
103. 103. dependent / independent variables
104. 104. regression analysis
105. 105. Least-squares estimating equation
106. 106. the coefficient of determination
107. 107. the coefficient of correlation</li></ul>DependentVariable<br />88<br />?<br />I<br />Independent Variable<br />Ŷ = a + bX<br />
108. 108. Least-squares estimating equation:<br /><ul><li>Review
109. 109. Chapter12:
110. 110. scatterdiagrams
111. 111. dependent / independent variables
112. 112. regression analysis
113. 113. Least-squares estimating equation
114. 114. the coefficient of determination
115. 115. the coefficient of correlation</li></ul>Ŷ = a + bX<br />
116. 116. Least-squares estimating equation:<br /><ul><li>Review
117. 117. Chapter12:
118. 118. scatterdiagrams
119. 119. dependent / independent variables
120. 120. regression analysis
121. 121. Least-squares estimating equation
122. 122. the coefficient of determination
123. 123. the coefficient of correlation</li></ul>Y = a + bX<br />a = Y - bX<br />
124. 124. Least-squares estimating equation:<br />therelationshipbetween the age of a truck and the annual repair expense?<br /><ul><li>Review
125. 125. Chapter12:
126. 126. scatterdiagrams
127. 127. dependent / independent variables
128. 128. regression analysis
129. 129. Least-squares estimating equation
130. 130. the coefficient of determination
131. 131. the coefficient of correlation</li></ul>a = Y - bX<br />Step 2:<br />Y = a + bX<br />Step 1:<br />Ŷ = 3.75 + 0.75 X<br />Step 6:<br />Step 4:<br />X=3<br />Y=6<br />6.75= 3.75 + 0.75 * 4<br />Step 7:<br />a = 6 - 0.75*3 = 3.75<br />Step 5:<br />If the city has a truck that is 4 years old, <br />Step 8:<br />the director could use the equation to predict \$675 annually in repairs. <br />
132. 132. Least-squares estimating equation:<br />Example:<br /><ul><li>To find the simple/linear regression of Personal Income (X) and Auto Sales (Y)</li></ul>If X=64, what about Y?<br /><ul><li>Review
133. 133. Chapter12:
134. 134. scatterdiagrams
135. 135. dependent / independent variables
136. 136. regression analysis
137. 137. Least-squares estimating equation
138. 138. the coefficient of determination
139. 139. the coefficient of correlation</li></ul>Step 1: <br />Count the number of values.      <br />N = 5<br />Step 2: <br />Find XY, X2   See the below table<br />
140. 140. Least-squares estimating equation:<br />Substitute in the above slope formula given.            <br />Slope(b) = = 0.19<br /> 1159.7-5*62.2*3.72<br />19359-5*62.2*62.2<br /><ul><li>Review
141. 141. Chapter12:
142. 142. scatterdiagrams
143. 143. dependent / independent variables
144. 144. regression analysis
145. 145. Least-squares estimating equation
146. 146. the coefficient of determination
147. 147. the coefficient of correlation</li></ul>Find ΣX, ΣY, ΣXY, ΣX2.            ΣX = 311 Mean = 62.2             ΣY = 18.6 Mean = 3.72<br />            ΣXY = 1159.7             ΣX2 = 19359 <br />Step 3: <br />Step 4: <br />
148. 148. Least-squares estimating equation:<br />            <br />Slope(b) = 0.19<br /><ul><li>Review
149. 149. Chapter12:
150. 150. scatterdiagrams
151. 151. dependent / independent variables
152. 152. regression analysis
153. 153. Least-squares estimating equation
154. 154. the coefficient of determination
155. 155. the coefficient of correlation</li></ul>Now, again substitute in the above intercept formula given.           <br /> Intercept(a) = Y - bX  = 3.72- 0.19 * 62.2= -8.098<br />Step 5: <br />Step 6: <br />Then substitute these values in regression equation formula            Regression Equation(Ŷ) = a + bX<br />         Ŷ  = -8.098 + 0.19X<br />Regression Equation:<br />Ŷ = a + bX            = -8.098 + 0.19(64)            = -8.098 + 12.16            = 4.06<br />Suppose if we want to know the approximate y value for the variable X = 64. Then we can substitute the value in the above equation.<br />
156. 156. Least-squares estimating equation:<br /> to minimize the sum of the squares of the errors to measure the goodness of fit of a line<br /><ul><li>Review
157. 157. Chapter12:
158. 158. scatterdiagrams
159. 159. dependent / independent variables
160. 160. regression analysis
161. 161. Least-squares estimating equation
162. 162. the coefficient of determination
163. 163. the coefficient of correlation</li></ul>SE<br />SE<br />ei = residuali<br />Strong<br />correlation<br />Weak<br />correlation<br />
164. 164. Least-squares estimating equation:<br /> to minimize the sum of the squares of the errors to measure the goodness of fit of a line<br /><ul><li>Review
165. 165. Chapter12:
166. 166. scatterdiagrams
167. 167. dependent / independent variables
168. 168. regression analysis
169. 169. Least-squares estimating equation
170. 170. the coefficient of determination
171. 171. the coefficient of correlation</li></ul>ei = residuali<br />
172. 172. Correlation Analysis:<br />describe the degree to which one variable is linearly related to another. <br /><ul><li>Review
173. 173. Chapter12:
174. 174. scatterdiagrams
175. 175. dependent / independent variables
176. 176. regression analysis
177. 177. Least-squares estimating equation
178. 178. the coefficient of determination
179. 179. the coefficient of correlation</li></ul>r 2<br />Coefficient of Determination:<br />Measure the extent, or strength, of the association that exists<br />between two variables. <br />r<br />Coefficient of Correlation:<br />Square root of coefficient of determination<br />
180. 180. r 2<br />Coefficient of Determination:<br />Measure the extent, or strength, of the association that exists between two variables. <br /><ul><li>Review
181. 181. Chapter12:
182. 182. scatterdiagrams
183. 183. dependent / independent variables
184. 184. regression analysis
185. 185. Least-squares estimating equation
186. 186. the coefficient of determination
187. 187. the coefficient of correlation
188. 188. 0 ≤ r2 ≤ 1.
189. 189. The larger r2 , the stronger the linear relationship.
190. 190. The closer r2 is to 1, the more confident we are in our prediction.</li></li></ul><li>r 2<br />Coefficient of Determination:<br /><ul><li>Review
191. 191. Chapter12:
192. 192. scatterdiagrams
193. 193. dependent / independent variables
194. 194. regression analysis
195. 195. Least-squares estimating equation
196. 196. the coefficient of determination
197. 197. the coefficient of correlation</li></li></ul><li>r<br />Coefficient of Correlation:<br />Square root of coefficient of determination<br /><ul><li>Review
198. 198. Chapter12:
199. 199. scatterdiagrams
200. 200. dependent / independent variables
201. 201. regression analysis
202. 202. Least-squares estimating equation
203. 203. the coefficient of determination
204. 204. the coefficient of correlation</li></li></ul><li>Review<br /><ul><li>Review
205. 205. Chapter12:
206. 206. scatterdiagrams
207. 207. dependent / independent variables
208. 208. regression analysis
209. 209. Least-squares estimating equation
210. 210. the coefficient of determination
211. 211. the coefficient of correlation</li></ul>Which value of r indicates a stronger correlation than 0.40? A. -0.30B. -0.50C. +0.38D. 0<br />If all the plots on a scatter diagram lie on a straight line, what is the standard error of estimate? A. -1B. +1C. 0D. Infinity<br />
212. 212. Review<br /><ul><li>Review
213. 213. Chapter12:
214. 214. scatterdiagrams
215. 215. dependent / independent variables
216. 216. regression analysis
217. 217. Least-squares estimating equation
218. 218. the coefficient of determination
219. 219. the coefficient of correlation</li></ul>In the least squares equation,  Ŷ = 10 + 20X the value of 20 indicates A. the Y intercept.B. for each unit increase in X, Y increases by 20.C. for each unit increase in Y, X increases by 20.D. none of these.<br /> <br />
220. 220. Review<br /><ul><li>Review
221. 221. Chapter12:
222. 222. scatterdiagrams
223. 223. dependent / independent variables
224. 224. regression analysis
225. 225. Least-squares estimating equation
226. 226. the coefficient of determination
227. 227. the coefficient of correlation</li></ul>A sales manager for an advertising agency believes there is a relationship between the number of contacts and the amount of the sales. To verify this belief, the following data was collected: <br />What is the Y-intercept of the linear equation? A. -12.201B. 2.1946C. -2.1946D. 12.201<br />
228. 228. What we have learnt?<br /><ul><li>scatterdiagrams
229. 229. dependent / independent variables
230. 230. regressionanalysis
231. 231. Least-squares estimatingequation
232. 232. the coefficient of determination
233. 233. the coefficient of correlation</li></li></ul><li>