Here is a Moving Distribution or a dynamic Regression Analysis
1) Set slider Sigma ( .2 , .4 ) and adjust slider " b " ; but Notice equation " Y " and the small range it takes on.
2) Y + Sum of X Y = 1
3) The equations - that by pure coincidence of arithmetic - have the relationship shown below for " Y " and " o "
4) " o " is the component of " Y " ; which, It is quite the surprise to have the sum of " Y " and " o " = 1
5) " o " is composed of the slider " sigma times ( -m times ( k + (k - a ) ) "
6) set Sigma = 0 ; this is the zero point
7) Set slider " b " all the way to the right to " - 1 " to have horizontal motion !
8) Set sigma at - 4.2 and " b " at -1.14