Consider the simple linear regression model yi =

d) (1 mark). Suppose a new data point, $n+11yn+1 arrives, and we want to update our sufcient statistics looking at the old data, which we have not stored. (This is useful for online learning.) We can show this for :E as follows n. + 1 1_ t n + 1 n+ 1 _ cn} + n + 1 (3%] _ 5(a)) This has the form: new estimate is old estimate plus correction. We see that the size of the correction diminishes over time (i.e., as we get more samples). Derive a similar expression to update 3]. e) ('2 maIkS). Show that one can update 013+\" recursively using 1 n+1 03+\" = 7n+11ln+1 + 1103;) + niinlg'} _ (n + 1)5:(\"+1)(\"+1}:| f) ('2 marks). Derive a similar expression to update Cm. g) (1 mark). What is the update expression for the estimate of g and [31 using only the updated sufcient statistics