#announce Calculating a population correlation coefficient.
              Population Correlation Coefficients
              ===================================


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


+----------------------------------------------------------------------------+
|    x           y            x^2              y^2              xy           |
+----------------------------------------------------------------------------+
#input mac_number,,Enter the number of points
#repeat #include correl.inc,,mac_number
[[d n=mac_number]]
----------------------------------------------------------------------------

 [[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   ]]