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1. (a) For a simple linear regression model covered in the lecture notes, derive the relationship between the coefficient of determination R and the sample correlation coefficient r given by r = EL(y: - 9)(1, - 2) (b) Consider a simple linear regression model with a known intercept pa- rameter 1= Pot Britt, i=l,..., n where & is known, 8 is an unknown slope parameter, errors , are uncorrelated with zero mean and common variance of. i. Find the least squares estimator of 8 (you must justify your an- swer). Does your estimator differ from the estimator obtained in lectures for the case where both &, and S, are unknown? ii. Find the mean and variance of the least squares estimator by (you must justify your answer)- ili. Find the maximum likelihood estimator of 8 (you must justify your answer). iv. Prove for the model above that the following identity holds where y; denotes the fitted value A + bir;. We are dealing with a partition of the variation around & rather than around y. Show that i=1 i=l i=I no longer holds