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The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature \(x_{1}\), the number of days in the month \(x_{2}\), the average product purity \(x_{3}\), and the tons of product produced \(x_{4}\). The past year's historical data are available and are presented in the following table. \begin{tabular}{ccccc} \(\boldsymbol{y}\) & \(\boldsymbol{x}_{1}\) & \(\boldsymbol{x}_{2}\) & \(\boldsymbol{x}_{3}\) & \(\boldsymbol{x}_{4}\) \\ \hline 240 & 25 & 24 & 91 & 100 \\ 236 & 31 & 21 & 90 & 95 \\ 290 & 45 & 24 & 88 & 110 \\ 274 & 60 & 25 & 87 & 88 \\ 301 & 65 & 25 & 91 & 94 \\ 316 & 72 & 26 & 94 & 99 \\ 300 & 80 & 25 & 87 & 97 \\ 296 & 84 & 25 & 86 & 96 \\ 267 & 75 & 24 & 88 & 110 \\ 276 & 60 & 25 & 91 & 105 \\ 288 & 50 & 25 & 90 & 100 \\ 261 & 38 & 23 & 89 & 98 \end{tabular} (a) Fit a multiple linear regression model using the above data (b) Predict power consumption for a month in which days, \(x_{3}=90 \%,\) and \(x_{4}=98\) \(x_{1}=75^{\circ} \mathrm{F}, x_{2}=24\) tons

An engineer at a semiconductor company wants to model the relationship between the device gain or \(\mathrm{hFE}(y)\) and three parameters: emitter-RS \(\left(x_{1}\right)\) base-RS \(\left(x_{2}\right),\) and emitter-to-base-RS \(\left(x_{3}\right) .\) The data are shown below: $$ \begin{array}{cccc} x_{1}, & x_{2}, & x_{3}, & y_{1} \\ \text { Emitter-RS } & \text { cBase-RS } & \text { E-B-RS } & \text { hFE- IM-5 } V \\ \hline 14.62 & 226.0 & 7.000 & 128.40 \\ 15.63 & 220.0 & 3.375 & 52.62 \\\ 14.62 & 217.4 & 6.375 & 113.90 \\ 15.00 & 220.0 & 6.000 & 98.01 \\ 14.50 & 226.5 & 7.625 & 139.90 \\ 15.25 & 224.1 & 6.000 & 102.60 \\ 16.12 & 220.5 & 3.375 & 48.14 \\ 15.13 & 223.5 & 6.125 & 109.60 \\ 15.50 & 217.6 & 5.000 & 82.68 \\ 15.13 & 228.5 & 6.625 & 112.60 \\ 15.50 & 230.2 & 5.750 & 97.52 \\\ 16.12 & 226.5 & 3.750 & 59.06 \\ 15.13 & 226.6 & 6.125 & 111,80 \\ 15.63 & 225.6 & 5.375 & 89.09 \\ 15.38 & 234.0 & 8.875 & 171.90 \ 15.50 & 230.0 & 4.000 & 66\. \end{array} $$ $$ \begin{array}{cccc} x_{1}, & x_{2}, & x_{3}, & y_{1} \\ \text { Emitter-RS } & \text { cBase-RS } & \text { E-B-RS } & \text { hFE-IM-5V } \\ 14.25 & 224.3 & 8.000 & 157.10 \\ 14.50 & 240.5 & 10.870 & 208.40 \\ 14.62 & 223.7 & 7.375 & 133.40 \end{array}$$ (a) Fit a multiple linear regression to the data. (b) Predict hFE when \(x_{1}=14\). \(x_{2}=220\), and \(x_{3}=5\). [Data from Myers and Montgomery (2002)]