2. Consider the following data set: X Y X Y 1 925 35 368 2 870 40 359 4 899 50 348 4 720 50 322 5 594 Here are the summaryr statistics: EX!- = 358, 2 X3 = 11554, Zack; = 159595, 2 K = 10588, 2 1:? = 6482016- A simple linear regression model K=u+1Xi+Es i=1,...,19, where e3; is normally.r distributed with mean 0 and constant variance on, is tted to the data. (a) Estimate g and 51 by least squares estimation. [3 marks] {13) Find an unbiased estimate of org. [4 marks] (e) Estimate the mean value of Y when X = 9 and hence construct a 95% condence interval for the mean of Y given X = 9. [5 marks] {d} Test for the lack of t at 1% level of signicance. [8 marks]