Another service from Omega

The Correlation Coefficient and the SD line


*****
> with(stats):
> x := [1,2,3,4,5,6,7]:
> describe[mean](x):
> AVE := x -> stats[describe,mean](x):
> AVE(x); 
                                  4
> SD := x -> stats[describe,standarddeviation](x):
> SD(x); 
                                  2
> y := [6,7,5,4,3,1,2]: 
                      y := [6, 7, 5, 4, 3, 1, 2]
> AVE(y); 
                                  4
> SD(y); 
                                  2
> r := (x,y) -> stats[describe,linearcorrelation](x,y): 
                                -13
                                 ---
                                 14
> with(statplots):
> scatter := (x,y) -> stats[statplots,scatter2d](x,y):
> scatter(x,y);
picture a picture here
> sdline := (x,d1,d2) -> AVE(d2)+sign(r(d1,d2))*(SD(d2)/SD(d1))*(x-AVE(d1)):
> with(plots):
> l1 := plot(sdline(u,x,y),u=0..10):
> scat := scatter(x,y):
> display({l1,scat});
picture a picture here

Compute the five number summary for the following data: x as before and y given by,

> yb := [2,1,4,3,7,5,6]:
> avex := AVE(x): sdx := SD(x): avey := AVE(yb): sdy := SD(yb): rb := r(x,yb):
> avex, sdx, avey, sdy, rb; 

                                             23
                                4, 2, 4, 2, ----
                                             28
> evalf(rb); 
                                  .8214285714
> l2 := plot(sdline(u,x,yb),u=0..10):
> scat2 := scatter(x,yb):
> display({l2,scat2});
picture a picture here
Link to the commands in this file
Carlos Rodriguez <carlos@math.albany.edu>
Last modified: Thu Feb 19 14:17:47 EST 1998