1. Consider the simple linear regression model: Yi = Bo + Bili + ; where ci N(0, 02). Suppose we have 10 data points of x and Y and from the data the following results are obtained. O 10 00 7 6 O O O LO O X 10 (x; - 3)2 - 27.515, En(yi - y)2 = 62.144 Zil(xi - x)(yi - y) = 31.408, x = 2.629, y = 7.374 (a) (2 marks) Obtain the least squares estimates Bo and B1. Using these estimates, obtain the fitted value y at x = 3. (b) (3 marks) The SSE value is given as E(yi - yi)2 = 26.293. Construct a 90% confidence interval for E(Y |x = 3). (c) (2 marks) Briefly comment on the goodness-of-fit of the fitted model. (d) (3 marks) Is the linear relationship between a and Y significant? Justify your answer by conducting an appropriate test at a = 0.05. (e) (2 marks) (Conceptual question) At a given x, briefly explain why (in general) a (1 - ) 100% confidence interval for E(Y|x) is narrower than a (1 -@) 100% prediction interval for Ynew (the new observed response value at x)