Robert Boyle (1627-1691) established the law that (pressure \(\times\) volume) \(=\) constant for a gas at a constant temperature. By pouring mercury into the open top of the long side of a \(\mathrm{J}\)-shaped tube, he increased the pressure on the air trapped in the short leg. The volume of trapped air \(=h \times\) cross section, where \(h\) is the height of the air in the short leg. If \(y=\) height of mercury, adjusted for the pressure of the atmosphere on the open end, then \(y\) and \(x=1 / h\) should obey a straight-line relationship.

(a) Fit a straight line by least squares to Boyle's data.

(b) Check the residuals for a possible violation of the assumptions.

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h 48 46 44 42 2 9 15 y 29 30. 31- 16 16 16 66 33 8 16 35 40 40 56 38 36 34 32 30 28 26 26 24 5 37 39- 41- 16 16 11 10 16 36 44- 47 16 16 50. 16 56 54- 16 56 13 58- 16 16