#announce Calculating a population correlation coefficient.
#define bump,,[[$1 $2=$2+1]] 
              Population Correlation Coefficients
              ===================================

Using The All New,Singing,Dancing and Swearing Scrivener.


5/8/85

[[def4.0]] [[de This is a comment the dlf%4.0f defines the format as floating point of field 4 ]]
[[d n=0]]

+----------------------------------------------------------------------------+
|    x           y            x^2              y^2              xy           |
+----------------------------------------------------------------------------+

 [[ x=10  ]]    [[ y=6 ]]    [[ x^2  ]]      [[ y^2  ]]      [[ x*y  ]] bump [s,,n]

 [[ x=7   ]]    [[ y=4 ]]    [[ x^2  ]]      [[ y^2  ]]      [[ x*y  ]] bump [s,,n]

 [[ x=12  ]]    [[ y=7 ]]    [[ x^2  ]]      [[ y^2  ]]      [[ x*y  ]] bump [s,,n]

 [[ x=12  ]]    [[ y=8 ]]    [[ x^2  ]]      [[ y^2  ]]      [[ x*y  ]] bump [s,,n]

 [[ x=9   ]]    [[ y=10]]    [[ x^2  ]]      [[ y^2  ]]      [[ x*y  ]] bump [s,,n]

 [[ x=16  ]]    [[ y=7 ]]    [[ x^2  ]]      [[ y^2  ]]      [[ x*y  ]] bump [s,,n]

 [[ x=12  ]]    [[ y=10]]    [[ x^2  ]]      [[ y^2  ]]      [[ x*y  ]] bump [s,,n]

 [[ x=18  ]]    [[ y=15]]    [[ x^2  ]]      [[ y^2  ]]      [[ x*y  ]] bump [s,,n]

 [[ x=8   ]]    [[ y=5 ]]    [[ x^2  ]]      [[ y^2  ]]      [[ x*y  ]] bump [s,,n]

 [[ x=12  ]]    [[ y=6 ]]    [[ x^2  ]]      [[ y^2  ]]      [[ x*y  ]] bump [s,,n]

 [[ x=14  ]]    [[ y=11]]    [[ x^2  ]]      [[ y^2  ]]      [[ x*y  ]] bump [s,,n]

 [[ x=16  ]]    [[ y=13]]    [[ x^2  ]]      [[ y^2  ]]      [[ x*y  ]] bump [s,,n]

----------------------------------------------------------------------------

 [[t   sx ]]    [[t   sy ]]  [[t sxs   ]]    [[t sys    ]]   [[t sxy  ]] 

===========================================================================


Population coefficient is given by           sum(xy) - sum(x)*sum(y)/n
                                    -------------------------------------------------
                                    sqr[((sum(x)^2)-(sum(x)^2)/n))*((sum(y)^2)-((sum(y)^2)/n)]


                                 =           [[o sxy ]] - [[o a= sx*sy/n]]
                                    ---------------------------------------
                                             sqr[ [[o b=sxs-((sx^2)/n)]] * [[o c=sys-((sy^2)/n)]] ]

[[def5.1]]
                                 =     [[o a=sxy-a]]
                                    ------------------ 
                                       [[o b=(b*c)^0.5 ]]


[[def5.4]]

                                 =  [[ a/b   ]]