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:
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  • 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&apos;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&apos;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&apos;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!
  • 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>

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