In Exercise 11.4 it would have been entirely reasonable to impose the condition \(\alpha=0\) before fitting a straight line by the method of least squares.

(a) Use the method of least squares to derive a formula for estimating \(\beta\) when the regression line has the form \(y=\beta x\).

(b) With reference to Exercise 11.4, use the formula obtained in part (a) to estimate \(\beta\) and compare the result with the estimate previously obtained without the condition that the line must pass through the origin.

Data From Exercise 11.4

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11.14 With reference to Exercise 11.3, express 90% limits of prediction for the tearing strength in terms of the temperature xo. Choosing suitable values of xo, sketch graphs of the loci of upper and lower limits of predic- tion on the diagram of part (a) of Exercise 11.3. Note that since any two sets of limits of prediction obtained from these bands are dependent, they should be used only for a single temperature xo.