Can you please help me know how to finish part a or where I went wrong. Also some insight for b and c would be appreciated. Thanks!

holds: [ (yi - y)2 = [ ( mi - 3)2 + [(yi - ji)2 SS(Total) SS( Reg) SS( Res) Note that SS(Res) is the sum of squared residuals as defined in class, and we shall define SS(Total) and SS( Reg) as shown in this equation (we'll discuss the significance of this decomposition later). [ Hint: Add and subtract pi in the SS(Total) term. ] (c) The "sample variance of the responses y1, ..., Un" and "estimated error variance (62)" are two different quantities. Explain, in a couple sentences, how these two quantities are related to terms seen in the sum of squares decomposition in (b). 2. [Derivation/Conceptual] Continue the setup given in question 1. (a) Verify that SS( Reg) [EL(Ti - )(yi - y)12 SS(Total) EL(ri -@) Z(yi -y)2 [ Hint: Write SS(Reg) in terms of B1 . ] (b) How is your result in (a) related to the sample correlation r between the mi's and yi's? Then if pi = yi for all i = 1, ..., n, what does that tell us about r and the fitted regression line? (c) We stated that when viewed as a random variable, SS(Res)/o' ~ X2_2. Use this fact to show that E(6-) = o', that is, the way we defined o' gives us an unbiased estimate of o'. You can look up and use any results about the chi-square distribution without proof.( 2 ; - ( ) ( yz - y ) n ( 9 - SC ) 2 ( 21 . - 5( ) ( y - 4) (2; - 30 )2 SIMS85(Rec) = 3 ( M: - y ) 2 2 = S( y - Bact B, C ; - y ( - BIC + Boc . ) = BS ( Total) = ( yi = y ) 2 ss ( Total )