(a) Using the table and the values of a and $b$ in the given relations. develop a Linear regression formula. $\zeta^{*}=\mathbf {a}+\mathbf{b} . \mathrm{X}$. where '' represents the yield of the field and $. \mathcal{}^{\prime}$ for the prevailing temperature $$ \text { Take a }=\frac{\left(\sum y ight)\left(\sum x^{2} ight)-\left(\sum x ight)\left( \sum x y ight)}{n\left("sum x^{2} ight)-\left(\sum x ight)^{2}} \quad \text { and } \quad \mathrm{b}=\frac{n\left(\sum x y ight)-\sum x \sum y} {n\left(\sum x^{2} ight)-\left(\sum x ight)^{2}} $$ \begin{tabular}{|c|cc|} \hline $\mathrm{S} / \mathrm{n}$ & Temperature $(\mathrm{X})$ & Yield $(\mathrm{Y})$ \hline 1 & 50 & 122 \hline 2 & 53 & 118 W \hline 3 & 54 & 128 \hline 4 & 55 & 121 1 \hline 5 & 56 & 125 W \hline 6 & 59 & 136 \hline 7 & 62 & 144 " \hline 8 & 65 & 142 W \hline 9 & 67 & 149 \hline 10 & 71 & 161 1 \hline \end{tabular) Use the model to estimate the (i) TEMPERATURE that produces the yield of 155 (ii) YIELD when the temperature is $77^{\circ} \mathrm{C}$. SP.JG. 102