3 The table shows the maximum weight, \(y _ { A }\) grams, of Salt \(A\) that will dissolve in 100 grams of water at various temperatures, \(x ^ { \circ } \mathrm { C }\).
| \(\boldsymbol { x }\) | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 60 | 70 | 80 |
| \(\boldsymbol { y } _ { \boldsymbol { A } }\) | 20 | 35 | 48 | 57 | 77 | 92 | 101 | 111 | 121 | 137 | 159 | 182 |
- Calculate the equation of the least squares regression line of \(y _ { A }\) on \(x\).
- The data in the above table are plotted on the scatter diagram on page 4.
Draw your regression line on this scatter diagram.
- For water temperatures in the range \(10 ^ { \circ } \mathrm { C }\) to \(80 ^ { \circ } \mathrm { C }\), the maximum weight, \(y _ { B }\) grams, of Salt \(B\) that will dissolve in 100 grams of water is given by the equation
$$y _ { B } = 60.1 + 0.255 x$$
- Draw this line on the scatter diagram.
- Estimate the water temperature at which the maximum weight of Salt \(A\) that will dissolve in 100 grams of water is the same as that of Salt B.
- For Salt \(A\) and Salt \(B\), compare the effects of water temperature on the maximum weight that will dissolve in 100 grams of water. Your answer should identify two distinct differences.
\section*{Temperatures and Maximum Weights}
\includegraphics[max width=\textwidth, alt={}]{91466019-8feb-4292-b616-e8e8667e2e54-4_2023_1682_404_173}