An engineer at a semiconductor company wants to model the relationship between the device HFE (y) and three parameters: Emitter-RS (x1), Base-RS (x2), and Emitter-to-Base RS (x3). The data are shown in the following table.
(a) Fit a multiple linear regression model to the data.
(b) Estimate σ2.
(c) Find the standard errors se.
(d) Predict HFE when x1 = 14.5, x2 = 220, and x3 = 5.0.

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X3 E-B-RS Emitter-RS Base-RS HFE-1M-5V 226.00 7.000 14.620 128.40 3.375 52.62 15.630 220.00 217.40 6.375 14.620 113.90 15.000 220.00 6.000 98.01 14.500 226.50 7.625 139.90 15.250 224.10 6.000 102.60 16.120 220.50 3.375 48.14 15.130 223.50 6.125 109.60 15.500 217.60 5.000 82.68 228.50 15.130 6.625 112.60 15.500 230.20 5.750 97.52 16.120 226.50 3.750 59.06 15.130 226.60 6.125 111.80 5.375 89.09 15.630 225.60 229.70 5.875 15.380 101.00 8.875 171.90 14.380 234.00 15.500 230.00 4.000 66.80 8.000 14.250 224.30 157.10 14.500 240.50 10.870 208.40 14.620 223.70 7.375 133.40