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represent predicted value Yh as a linear function of the observations Y1, Y2, ..., Yn


a} Represent the predicted value 17}, as a linear function of the observations 1’,13,...,}; and
derive the mean and variance of 1% using the fact that for an}.r constants a1,az,...,an and
independent observations Y,I§,...,I; where I”; ~ Ngupo'fl), E‘lz gig} : Edi-Jul and V‘lZani} : Ear-20}?
i=1 i=1 i=1 i=1
b) Show the steps to conclude under normality of errors that it as; +51%) ~ t
, (H:
35?. l where {(#2) represent the student's t—random variable 1with (n-Z) degrees of fi'eedorn. C) Use the formula for 0'2 {ii} to derive the expression for 0'2 {b0}.

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