Lesson04
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Statistics for International Business School, Hanze University of Applied Science, Groningen, The Netherlands
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Lesson04
- 1. IBS Statistics Year 1 Dr. Ning DING n.ding@pl.hanze.nl I.007
- 3. Chapter12: Simple Regression and Correlation
- 4. dependent / independent variables
- 8. the coefficient of determination
- 10. Chapter12: Simple Regression and Correlation
- 11. ExercisesFind the interquartile range: 1460 1471 1637 1721 1758 1787 1940 2038 2047 2054 2097 2205 2287 2311 2406 Interquartile Range =Q3-Q1 =2205-1721 =484
- 13. Chapter12: Simple Regression and Correlation
- 14. ExercisesL=(8+1)*25%=2.25 Q1=133.5 Interquartile Range =274.5-133.5 =141 L=(8+1)*75%=6.75 Q3=274.5
- 15. Review Median Quartile Decile Percentile 1 2 2 4 1 2 2 4 5 7 8 9 12 1st D Q1=2 Interquartile Range 5 7 8 9 12 Q3=8.5 9th D Boxplot How to interpret? http://cnx.org/content/m11192/latest/
- 17. Chapter12: Simple Regression and Correlation
- 18. ExercisesMean= € 450 a b € 20 € 2000 Q1= € 250 Q3= € 850 Median= € 350 The distribution is skewed to __________ because the mean is __________the median. the right larger than http://cnx.org/content/m11192/latest/
- 19. 0.8 1.0 1.0 1.2 1.2 1.3 1.5 1.7 2.0 2.0 2.1 2.2 4.0 Review Mean > Median 2.0 3.2 3.6 3.7 4.0 4.2 4.2 4.5 4.5 4.6 4.8 5.0 5.0 Mean < Median Positively skewed http://qudata.com/online/statcalc/ Negatively skewed
- 20. Review This means that the data is symmetrically distributed. Zero skewness mode=median=mean
- 22. Chapter12:
- 23. scatterdiagrams
- 24. dependent / independent variables
- 27. the coefficient of determination
- 28. the coefficient of correlation
- 29. scatterdiagrams
- 30. dependent / independent variables
- 33. the coefficient of determination
- 35. Chapter12:
- 36. scatter diagrams
- 37. dependent / independent variables
- 40. the coefficient of determination
- 41. the coefficient of correlation
- 43. Chapter12:
- 44. scatterdiagrams
- 45. dependent / independent variables
- 48. the coefficient of determination
- 49. the coefficient of correlationScatter Diagram: Positive correlation
- 51. Chapter12:
- 52. scatterdiagrams
- 53. dependent / independent variables
- 56. the coefficient of determination
- 57. the coefficient of correlationScatter Diagram: Negative correlation
- 59. Chapter12:
- 60. scatterdiagrams
- 61. dependent / independent variables
- 64. the coefficient of determination
- 65. the coefficient of correlationScatter Diagram: No correlation
- 67. Chapter12:
- 68. scatterdiagrams
- 69. dependent / independent variables
- 72. the coefficient of determination
- 74. If related, we can describe the relationshipWeak & Positive correlation Strong & Positive correlation No correlation Weak & Negative correlation Strong & Negative correlation
- 76. Chapter12:
- 77. scatterdiagrams
- 78. dependent / independent variables
- 81. the coefficient of determination
- 82. the coefficient of correlation
- 84. Dependent variables: to predictVariables: DependentVariable Independent Variable
- 86. Chapter12:
- 87. scatterdiagrams
- 88. dependent / independent variables
- 91. the coefficient of determination
- 94. Chapter12:
- 95. scatterdiagrams
- 96. dependent / independent variables
- 99. the coefficient of determination
- 101. Chapter12:
- 102. scatterdiagrams
- 103. dependent / independent variables
- 104. regression analysis
- 106. the coefficient of determination
- 107. the coefficient of correlationDependentVariable 88 ? I Independent Variable Ŷ = a + bX
- 109. Chapter12:
- 110. scatterdiagrams
- 111. dependent / independent variables
- 112. regression analysis
- 114. the coefficient of determination
- 115. the coefficient of correlationŶ = a + bX
- 117. Chapter12:
- 118. scatterdiagrams
- 119. dependent / independent variables
- 120. regression analysis
- 122. the coefficient of determination
- 123. the coefficient of correlationY = a + bX a = Y - bX
- 125. Chapter12:
- 126. scatterdiagrams
- 127. dependent / independent variables
- 128. regression analysis
- 130. the coefficient of determination
- 131. the coefficient of correlationa = Y - bX Step 2: Y = a + bX Step 1: Ŷ = 3.75 + 0.75 X Step 6: Step 4: X=3 Y=6 6.75= 3.75 + 0.75 * 4 Step 7: a = 6 - 0.75*3 = 3.75 Step 5: If the city has a truck that is 4 years old, Step 8: the director could use the equation to predict $675 annually in repairs.
- 133. Chapter12:
- 134. scatterdiagrams
- 135. dependent / independent variables
- 136. regression analysis
- 138. the coefficient of determination
- 139. the coefficient of correlationStep 1: Count the number of values. N = 5 Step 2: Find XY, X2 See the below table
- 141. Chapter12:
- 142. scatterdiagrams
- 143. dependent / independent variables
- 144. regression analysis
- 146. the coefficient of determination
- 147. the coefficient of correlationFind ΣX, ΣY, ΣXY, ΣX2. ΣX = 311 Mean = 62.2 ΣY = 18.6 Mean = 3.72 ΣXY = 1159.7 ΣX2 = 19359 Step 3: Step 4:
- 149. Chapter12:
- 150. scatterdiagrams
- 151. dependent / independent variables
- 152. regression analysis
- 154. the coefficient of determination
- 155. the coefficient of correlationNow, again substitute in the above intercept formula given. Intercept(a) = Y - bX = 3.72- 0.19 * 62.2= -8.098 Step 5: Step 6: Then substitute these values in regression equation formula Regression Equation(Ŷ) = a + bX Ŷ = -8.098 + 0.19X Regression Equation: Ŷ = a + bX = -8.098 + 0.19(64) = -8.098 + 12.16 = 4.06 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.
- 157. Chapter12:
- 158. scatterdiagrams
- 159. dependent / independent variables
- 160. regression analysis
- 162. the coefficient of determination
- 163. the coefficient of correlationSE SE ei = residuali Strong correlation Weak correlation
- 165. Chapter12:
- 166. scatterdiagrams
- 167. dependent / independent variables
- 168. regression analysis
- 170. the coefficient of determination
- 171. the coefficient of correlationei = residuali
- 173. Chapter12:
- 174. scatterdiagrams
- 175. dependent / independent variables
- 176. regression analysis
- 178. the coefficient of determination
- 179. the coefficient of correlationr 2 Coefficient of Determination: Measure the extent, or strength, of the association that exists between two variables. r Coefficient of Correlation: Square root of coefficient of determination
- 181. Chapter12:
- 182. scatterdiagrams
- 183. dependent / independent variables
- 184. regression analysis
- 186. the coefficient of determination
- 187. the coefficient of correlation
- 188. 0 ≤ r2 ≤ 1.
- 189. The larger r2 , the stronger the linear relationship.
- 191. Chapter12:
- 192. scatterdiagrams
- 193. dependent / independent variables
- 194. regression analysis
- 196. the coefficient of determination
- 198. Chapter12:
- 199. scatterdiagrams
- 200. dependent / independent variables
- 201. regression analysis
- 203. the coefficient of determination
- 205. Chapter12:
- 206. scatterdiagrams
- 207. dependent / independent variables
- 208. regression analysis
- 210. the coefficient of determination
- 211. the coefficient of correlationWhich value of r indicates a stronger correlation than 0.40? A. -0.30B. -0.50C. +0.38D. 0 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
- 213. Chapter12:
- 214. scatterdiagrams
- 215. dependent / independent variables
- 216. regression analysis
- 218. the coefficient of determination
- 219. the coefficient of correlationIn 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.
- 221. Chapter12:
- 222. scatterdiagrams
- 223. dependent / independent variables
- 224. regression analysis
- 226. the coefficient of determination
- 227. the coefficient of correlationA 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: What is the Y-intercept of the linear equation? A. -12.201B. 2.1946C. -2.1946D. 12.201
- 229. dependent / independent variables
- 230. regressionanalysis
- 232. the coefficient of determination
Notes de l'éditeur
- Correlation and CauseJust because two variables are correlated, does not mean that one of the variables is the cause of the other. It could be the case, but it does not necessarily follow: There is a strong positive correlation between the number of cigarettes that one smokes a day and one's chances of contracting lung cancer (measured as the number of cases of lung cancer per hundred people who smoke a given number of cigarettes). The percentage of heavy smokers who contract lung cancer is higher than the percentage of light smokers who develop the disease, and both figures are higher than the percentage of non-smokers who get lung cancer. In this case, the cigarettes are definitely causing the cancer. There is a strong negative correlation between the total number of skiing holidays that people book for any month of the year and the total amount of ice cream that supermarkets sell for that month. This means that the more skiing holidays that are booked, the less ice cream is sold. Is there a cause here? Are people spending so much money on ice cream that they can't afford skiing holidays? Is the fact that the ice cream is so cold putting people off skiing? Clearly not! The simple fact is that most people tend to book their skiing holidays in the winter, and they tend to buy ice cream in the summer. Although a correlation between two variables doesn't mean that one of them causes the other, it can suggest a way of finding out what the true cause might be. There may be some underlying variable that is causing both of them. For instance, if a survey found that there is a correlation between the time that people spend watching television and the amount of crime that people commit, it could be because unemployed people tend to sit around watching the television, and that unemployed people are more likely to commit crime. If that were the case, then unemployment would be the true cause!