hello, im confused about the case where beta_0 is a known parameter. Thank you!

(b) Consider a simple linear regression model with a known intercept pa- rameter yi =0+lri+5ii 1': 1,...,'n. Where ,80 is known, 51 is an unknown slope parameter, errors 5': are uncorrelated with zero mean and common variance or . i. iii. iv. 2 Find the least squares estimator of {3, (you must justify your an swer). Does your estimator differ from the estimator obtained in lectures for the case where both 50 and 61 are unknown? . Find the mean and variance of the least squares estimator b1 (you must justify your answer). Find the maximum likelihood estimator of {31 (you must justify your answer). Prove for the model above that the following identity holds 2(a- Bar = 2(a- 50)\" + By.- m2, i=1 where 3; denotes the tted value ,60 + blIi- We are dealing with a partition of the variation around ,8.) rather than around 3). Show that 2'3" m2 = 26:: - a)? + Zen 9:02 no longer holds