Could you solve Question B part iii

Question 1. Consider a simple linear regression model with no intercept yi =13 +55\" i=1,...,n, {I} where ,81 is a slope parameter, enters 5.5 are uncorrelated with zero mean and common van'ance 02. to} [12 marks] i. Drove for the model (1) above that the runoamenoar identity no longer holds, that is, T! n n - s L _ 2 - s Zita -v) at Zia-s - at) +22%: we} i=1 i=1 i=1 in general, where 3'}; denotes the tted value 5131-. ii. Prove forthe model {1} above that the following identity holds \" 2 n 2 n 2 23,: = 23:3; +Ztvt F]- i=1 i=1 i=1 It shows partitioning of the variation around zero rather than around . Using this identity, suggest how to dene R2 for the model without an intercept. iii. The appropriate estimator of error variance is in model (1} is -2 _ 223:1[1'33 _ )2 0' 13] I where fitted values are given by ri- = blag. Show that 62 is unbiased for 0'2. If you are told that when errors are Nm, 93 ) and independent then (1?. _ 1}? 2 2 N xnl 0' independently.r of 11 show that b1 - :51 5'!\" v\" 2&1 3t has a t distribution with n 1 degrees of freedom. Hence derive a 100(1 (1)93 condence interval for 31. Suggest a statistic with an F1 n_1 distn'bution which can he used Tortesting the null hypothesis that 31 = {1 against the alternative H1 : ,61 7E 0