Question

Prove:
(?) ???=Σ ( ?−?̅  )² =Σ ?²−[(Σ ?²)/n] (Sum Squares X)

(?) ???=Σ( ?−?̅ )²=Σ ?²−[(Σ ?²)/?] (Sum Squares Y)

(?) ??? =Σ( ?−?̅ ) ( ?−?̅ )=Σ ??−[(Σ?)(Σ?)?] (Sum Products X,Y)

Answer 1

Solution:

Part a)

where

which can be rewritten as:

......equation i)

Thus solving square term, we get:

From equation i) , we can write and sum of

Since is constant.

thus we get:

. Hence Proved.

Part b)

where

which can be rewritten as:

......equation ii)

Thus solving square term, we get:

From equation ii) , we can write and sum of

Since is constant.

thus we get:

. Hence Proved.

Part c)

Hence Proved.