You are investigating the solubility of xylose in water inside a pumping system. The water is pressurized, so you get temperatures well in excess of \(200^{\circ} \mathrm{C}\). The variables are temperature \((x)\) and (maximum) grams of xylose per liter \((y)\). Your measurements are

Present your conclusion in the form of a linear regression line, with uncertainty. Indicate a \(90 \%\) credible interval for solubility at \(100^{\circ} \mathrm{C}\). Also indicate a \(90 \%\) predictive interval for a measurement of the solubility at \(100^{\circ} \mathrm{C}\). Explain the difference between the two.

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x (C) 24 42 62 83 103 124 143 164 185 y (g/L) 497 811 1061 1592 2190 2543 3131 3601 4236