The leastsquares propertyofthemeanstatesthatthedatafallcloserto y than toany other number c, inthesensethat i (yi y)2

Question:

The leastsquares propertyofthemeanstatesthatthedatafallcloserto ¯y than toany other number

c, inthesensethat

Σ

i

(yi − ¯y)2 <Σ

i

(yi − c)2.

Provethispropertybytreating f

(c) = Σi(yi − c)2 as afunctionof c and derivingthe valueof c that minimizesit.

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