# 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);
> 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});

## 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});

Link to the commands in this file
Carlos Rodriguez <carlos@math.albany.edu>