STA302H1 Midterm: UTSG STA 302 exsolf07
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Student number: there are 20 pages including this page, the last page is a table of formulae that may be useful. 1: consider the simple linear regression model. Yi = 0 + 1xi + i i = 1, . , n where the i are independent and identically distributed n (0, 2) random variables. Let b0 and b1 be the least squares estimates of 0 and 1 respectively. (a) (3 marks) what is the distribution of b1? (just state it. You do not have to derive anything for this part. ) Sxx! (b) (3 marks) let xh be a value of the predictor variable that is of interest. Show that var(b0 + b1xh) = 2(cid:18) 1 n + (xh x)2. You may use any formulae on the formula sheet that you nd useful except the formula for var( yh). Var(b0 + b1xh) = var(b0) + x 2 hvar(b1) + 2xhcov(b0, b1)
