3.81. The leastsquares property of the mean states that the data fall closer to y than to any other number

c, in the sense that the sum of squares of deviations of the data about their mean is smaller than the sum of squares of their deviations about c.

That is, 2(y/ - y)2

< 'Ziyi - c)2

.

Ifyou have studied calculus, prove this property by treating/

(c) = S(y,- — c)2 as a function of c and deriving the value of c that provides a minimum.

(Hint: Take the derivative of/

(c) with respect to c and set it equal to zero.)