Base equation in a linear regression.

[paroxsitic]

A = -8X + X^2 + 16

I am trying to find the following:
-8(X+Y) + (X+Y)^2 + 16, where Y will gradually increase and the sum will be taken.

For example. Lets assume Y=4

F(4) = -8(X+1) + (X+1)^2 + 16 + -8(X+2) + (X+2)^2 + 16 + -8(X+3) + (X+3)^2 + 16 + -8(X+4) + (X+4)^2 + 16
F(2) = -8(X+1) + (X+1)^2 + 16 + -8(X+2) + (X+2)^2 + 16


What an equation I can use to find the Sum of the above equation for any number Y.

 

[Deleted member 4993]

A = -8X + X^2 + 16

I am trying to find the following:
-8(X+Y) + (X+Y)^2 + 16,

= (X + Y - 4)[sup:1ewiko9q]2[/sup:1ewiko9q].................Does that tell you something?

where Y will gradually increase and the sum will be taken.

For example. Lets assume Y=4

F(4) = -8(X+1) + (X+1)^2 + 16 + -8(X+2) + (X+2)^2 + 16 + -8(X+3) + (X+3)^2 + 16 + -8(X+4) + (X+4)^2 + 16
F(2) = -8(X+1) + (X+1)^2 + 16 + -8(X+2) + (X+2)^2 + 16


What an equation I can use to find the Sum of the above equation for any number Y.

 

[paroxsitic]

I figured out the solution with help from #math at IRC.


xy(x+y-7) + y(73-21y+2yy)/6

 

[Denis]

"Doing" y = 1 to 9 shows the pattern clearly :
1: x^2 - 6x + 9
2: x^2 - 4x + 4
3: x^2 - 2x + 1
4: x^2 - 0x + 0
5: x^2 + 2x + 1
6: x^2 + 4x + 4
7: x^2 + 6x + 9
8: x^2 + 8x + 16
9: x^2 +10x + 25

So formula needs "sum of first (y-4) evens" and "sum of 1st (y-4) squares",
along with x^2(y) and an adjustment for the 1st 3 terms: -12x + 14; so:

x^2y + xk + k(2y-7)/6 - 12x + 14 where k = (y-4)(y-3)

Your formula (which works fine) is a re-arrangement of above.

 

[mmm4444bot]

I figured out the solution ...

I'm writing a book. What part did you figure out?

Cheers,

~ Mark