Minimum Bias: Fox Problem at page 9b

[CASPart5]

The problem is about using Additive Model, Least Squares Method. Fox solution uses a formula based approach. With so many formulae in part9 syllabus already, I'm trying to rely on first principles to solve this problem (rather than memorizing formulae), but for some reason I'm getting a wrong answer below. Can anyone please elaborate what is wrong with my approach:

si: row relativity
hj: column relativity

Initial values: s1 = 130, s2=50

Total losses=
62,500 157,500 30,000
90,000 41,250 112,500

Total Indicated Pure Premium=
125(200+s1+h1) 350(200+s1+h2) 75(200+s1+h3)
300(200+s2+h1) 150(200+s2+h2) 450(200+s2+h3)

SSE=
(125s1 + 125h1-37,500)^2 + (350s1 + 350h2 - 87,500)^2 +
(75s1 + 75h3 - 15,000)^2 + (300s2 + 300h1 - 30,000)^2 + (150s2 + 150h2 - 11,250)^2
+ (450s2 + 450h3 - 22,500)^2

Partial derivative of SSE w.r.t h1 gives:

2(125s1 + 125h1 - 37,500)(125) + 2(300s2 + 300h1 - 30,000)(300) = 0

Putting initial values of s1 and s2 in above equation, we get:

h1= 67.7514

However, fox's formula based solution comes up with h1=85.294

Can someone please explain what am I missing here?

Thank you so much for your time.

[CtrlAltDelete]

Originally Posted by CASPart5

SSE=
(125s1 + 125h1-37,500)^2.

The bold should be 75,000. I didn't bother checking the rest, you should do it yourself.

[CASPart5]

Thanks CtrlAltDelete!

The way I'm getting 37,500 is:

125*200: from Total Indicated Pure Premium
MINUS
62,500: from Total losses

Can you please elaborate how did you get 75,000?

Thanks,

[Jing.only]

I am confused by this question too.
But I figured out a way to get the answer

if you take the lost cost and reduce the base rate to get a (300 250 200 100 75 50) with (x1+y1 X1+y2 X1+y3 X2+y1 x2+y2 X2+y3)
sse=125*(x1+y1-300)^2+350*(x1+y2-250)^2+.....
then you will get the same answer...

[CASPart5]

thanks Jing! for taking time & answering...

[llcooljabe]

I clicked on this thread before looking at the subsection. I thought this was political and the topic was Fox News. Carry on.