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

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