SOLUTION: show that sum of (xi-a)^2=sum of (xi-x bar)^2+n(x bar -a)^2

Question 1121817: show that sum of (xi-a)^2=sum of (xi-x bar)^2+n(x bar -a)^2
Answer by Alex.33(110) (Show Source): You can put this solution on YOUR website!
x bar=X.
3.SUM[(xi-a)^2]=SUM[xi^2]+na^2-2a*(SUM[xi])=SUM[xi^2]+na^2-2anX
1.SUM[(xi-X)^2]=SUM[xi^2]+nX^2-2X*SUM[xi]=SUM[xi^2]+nX^2-2nX^2=SUM[xi^2]-nX^2
2.n(X-a)^2=nX^2+na^2-2anX.
1+2=3. Done.

RELATED QUESTIONS
(x + 2yi)^2 =... (answered by advanced_Learner)

need to know how to solve the equation for least square regression line y-hat = b0+b1X (answered by stanbon)

simplify in the form of... (answered by stanbon)

n object, that remains at rest, is acted upon by three forces F1, F2 and F3. The... (answered by Fombitz)

. Find E(x), E(X2) and 2 for the probability function P(x) defined by the... (answered by oscargut)

8. solve for x: (3 + 2i) + (4 + xi) = 7 - 5i 9. Which of the following is not... (answered by stanbon,user_dude2008)

Sum i1-7(i-1)^3? Sum i0-100[1/k-1/k+1]? Sum i2-3(xi+2)/xi? Sum i1-6(3i-2)? Sum... (answered by Alan3354)

A polynomial or degree3, with integer coefficients that has zeros root3i and o is :... (answered by Edwin McCravy)

The flow of traffic through a network of streets is show below in vehicles per hour.... (answered by estron7)