Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
IBS Statistics<br />Year 1<br />Dr. Ning DING <br />n.ding@pl.hanze.nl<br />I.007<br />
What we are going to learn?<br /><ul><li>Review
Chapter12: Simple Regression and Correlation
dependent / independent variables
scatterdiagrams
regressionanalysis
Least-squares estimatingequation
the coefficient of determination
the coefficient of correlation</li></li></ul><li>Review<br /><ul><li>Review
Chapter12: Simple Regression and Correlation
Exercises</li></ul>Find the interquartile range:<br /> <br />1460<br />1471<br />1637<br />1721<br />1758<br />1787			<br ...
Review EXCEL Lesson<br /><ul><li>Review
Chapter12: Simple Regression and Correlation
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....
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 />...
Review<br /><ul><li>Review
Chapter12: Simple Regression and Correlation
Exercises</li></ul>Mean= € 450<br />a<br />b<br />€ 20<br />€ 2000<br />Q1= € 250<br />Q3= € 850<br />Median= € 350<br />T...
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 />Revie...
Review<br />This means that the data is symmetrically distributed. <br />Zero skewness<br />mode=median=mean<br />
Chapter 12<br /><ul><li>Review
Chapter12:
scatterdiagrams
dependent / independent variables
regressionanalysis
Least-squares estimatingequation
the coefficient of determination
the coefficient of correlation
scatterdiagrams
dependent / independent variables
regressionanalysis
Least-squares estimatingequation
the coefficient of determination
the coefficient of correlation</li></li></ul><li>Regression and Correlation Analyses<br /><ul><li>Review
Chapter12:
Upcoming SlideShare
Loading in …5
×

Lesson04

2,923 views

Published on

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

Published in: Technology
  • Be the first to comment

  • Be the first to like this

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>

×