Mathematics problem

圖片參考：http://i17.tinypic.com/2hxn3bn.jpg

(i)
E(x)=E(55+1.2y)
40=55+1.2E(y)
E(y)=-12.5
(ii)
covariance Cov(x,y)
=E(xy)-E(x)E(y)
=E(55y+1.2y^2)+500
=55E(y)+1.2E(y^2)+500
=55E(y)+1.2[E(y)^2+Var(y)]+500
=55(-12.5)+1.2[(-12.5)^2+6.8^2]+500
=55.488
(iii)
correlation
=Cov(x,y)/[s(x)s(y)]
=55.488/(9.5*6.8)
=0.8589
(iv)
let y=a+bx
b
=Cov(x,y)/Var(y)
=55.488/(6.8^2)
=1.2
E(y)=a+bE(x)
-12.5=a+1.2(40)
a=-60.5
The linear regression line is
y=-60.5+1.2x
Hope it right !!

2007-02-22 20:00:10 補充：
Sorry,調轉方向b=Cov(x,y)/Var(x)=55.488/(9.5^2)=0.6148E(y)=a+bE(x)-12.5=a+0.6148(40)a=-37.09The linear regression line isy=-37.09+0.6148x