2.1 Consider the following five observations. You are to do all the parts of this exercise using only a calculator.

(a) Complete the entries in the table. Put the sums in the last row. What are the sample means i and y?

(b) Calculate b1 and D2 using (2.7) and (2.8) and state their interpretation.

(c) Compute L?:p?,Ii=rxiyi.Using these numerical values show that I(", - x)2 :Lx! - Nt' and I(r, - l)(yi - y) -Lxtyr - Nxy

(d) Use the least squarese stimatesf rom part

(b) to computet he fitted valueso fy, and complete the remainder of the table below. Put the sums in the last row.

(e) On graph paper, plot the data points and sketch the fitted regression line ji: h t b2xi.
(0 On the sketch in part (e), locate the point of the means ("r, y). Does your fitted line pass through that point? If not, go back to the drawing board, literally.
(g) Show that for these numerical values ! : h -l bzZ.
(h) Show thatf or thesen umericalv alues9 : y, wherei :2i,lt'l .
(i) Compute 62.
() Compute var(b2).

X (x-3) (x-x1(x-3) 3 5 2 2 | 3. -1 2 0 = -2 = lx-3)= == - (y-3) = - ()()