Put the scatter diagrams in order of strength of

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					                               Correlations




                          A                                     B




                          C                                     D




                          E                                     F


Put the scatter diagrams in order of strength of correlation:




                              increasing correlation

Remember correlation is a measure of linear association; ie it measures how
near the points are to being in a straight line.
Regression
Least squares regression line of y on x
(used for predicting values of y from values of x)
                             S       ( xi − x ) ( yi − y )
 y − y = b( x − x ) where b = xy =
                             S xx         ( xi − x ) 2


Pearson’s Product moment Correlation Coefficient
(measure of how close the points are to a straight line)
      S xy           ( xi −x )( yi − y )
r=             =
     S xx S yy     ( xi −x ) 2 ( yi − y ) 2


Spearman’s Rank Correlation Coefficient
(measure of whether one variable goes up as the other one does)
          6 di 2
rs = 1 −            where di = xi − yi , and xi and yi denote ranks of data
         n(n 2 − 1)
(This formula uses ranks of the data; the others use the actual data)


Big S (used in the above calculations)
For a sample of n pairs of observations ( xi , yi )
                               ( xi ) 2
S xx = ( xi − x ) = xi −
                 2          2
                                         = xi 2 − nx 2
                                  n
                                ( yi ) 2
S yy = ( yi − y ) = yi −
                 2           2
                                         = yi 2 − ny 2
                                  n
                                        ( xi )( yi )
S xy = ( xi − x )( yi − y ) = xi yi −                  =     xi yi − n ( x )( y )
                                             n
   r = 0.9541, rS = 1




r = 0.2405, rS = 0.2939




r = 0.4856, rS = 0.1515




r = 0.7366, rS = 0.6939




r = 0.5583, rS = −0.1848
          Samples of teenage girls. Foot length and height in cm.
         Sample A                                       Sample B
Height       Foot length                      Height           Foot length
         150             24                             160              22
         155             26                             148              23
         152             25                             160              23
         160             23                             161              23
         149            23.5                            158              24
         144            22.5                            153              21
         135             21                             173              26
         141             21                             162              24
         163             21                             176             22.5
         142             21                             173             22.5
         165             25                             164              26
         157             25                             160              23

         Sample C                                        Sample D
Height       Foot length                      Height         Foot length
         163             25                              155             23
         161             23                             155                  23
         152             25                             160                  23
         179             24                             179                  24
         163            25.5                            167                  25
         153             23                             163                  22
         155             22                             139                  23
         151            22.5                            163                  22
         142             21                             118                  19
         170             24                             157                  24
         160             23                             160                  23
         161             25                             146                  21

         Sample E                                        Sample F
Height       Foot length                      Height         Foot length
         160             23                             146              21
         158             24                             179              24
         164             24                             162              24
         155             21                             164              24
         173             26                             150             22.5
         163            25.5                            156              23
         156             24                             118              19
         157             22                             159              24
         151            22.5                            164              26
         163             22                             160              23
         164             26                             145              21
         160             23                             146              21