Question: is stated in the lecture notes (Lecture 2) that the least squares estimates for the linear regression of {yi}n i=1 on {xi}n i=1, 0 and

is stated in the lecture notes (Lecture 2) that the least squares estimates for the linear regression of {yi}n i=1 on {xi}n i=1, 0 and 1, are linear functions of the yi's: 0 = n i=1 ciyi, 1 = n i=1 diyi where {ci}n i=1 and {di}n i=1 are functions of {xi}n i=1 but do not depend on {yi}n i=1. (a) Find expressions for ci and di in terms of the predictor variate {xi}n i=1. (b) Under the simple linear regression model with responses {Yi}n i=1 and predictors {xi}n i=1, show that the least squares estimators 0 = n i=1 ciYi, 1 = n i=1 diYi are normally distributed random variables with mean parameters 0 and 1 re- spectively. Hint: apply another result from the Lecture 2 notes

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