Use the definitions

\\\\bar{x} =(1)/(n)\\\\sum x_(i)

and

s_(x)^(2)=(1)/(n)\\\\sum (x_(i)-(\\\\bar{x} ))^(2)

to show that if

Y_(i)=

\

a+bx_(i)

, then\ (a)

/bar (Y)=a+b\\\\bar{x}

and

s_(Y)^(2)=(1)/(n)\\\\sum (Y_(i)-(/bar (Y)))^(2)=b^(2)s_(x)^(2)

; (3 pts)\ (b) If

Z_(i)=(x_(i)-(\\\\bar{x} ))/(s_(x))

, then

/bar (Z)=0

and

s_(z)^(2)=1.(3pts)

Use the definitions X=n1Xi and sX2=n1(XiX)2 to show that if Yi= a+bXi, then (a) Y=a+bX and sY2=n1(YiY)2=b2sX2; (3 pts) (b) If Zi=sXXiX, then Z=0 and sz2=1.(3pts)