for what value of c is the quantity sigma(Xi-c)^2 minimized?

[Hint: Take the derivative with respect to c , set equal to 0 and solve]

I don't know where to start...

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- Mar 11th 2010, 05:12 PMquestionboyMaximising a sum of squared differences.
for what value of c is the quantity sigma(Xi-c)^2 minimized?

[Hint: Take the derivative with respect to c , set equal to 0 and solve]

I don't know where to start... - Mar 11th 2010, 05:54 PMmr fantastic
Start by noting that

$\displaystyle \sum_{i = 1}^n (X_i - c)^2 = \sum_{i = 1}^n (X_i^2 - 2 c X_i - c^2) = \sum_{i = 1}^n X_i^2 - 2 c \sum_{i = 1}^nX_i - \sum_{i = 1}^n c^2$

$\displaystyle = \sum_{i = 1}^n X_i^2 - 2 c \sum_{i = 1}^nX_i - n c^2$

and then use the hint. - Mar 11th 2010, 07:19 PMquestionboy
Thank you Mr fantastic

Do I set derivative of C equal to zero? - Mar 11th 2010, 11:16 PMmatheagle
why don't you use the hint.........

Take the derivative with respect to c , set equal to 0 and solve

$\displaystyle {d\over dc} \sum_{i=1}^n(X_i-c)^2=-2 \sum_{i=1}^n(X_i-c)=-2(n\bar X-nc)$

set this equal to zero, shows that $\displaystyle c=\bar X$

And it is a min, that's why you should obtain the second derivative.