Consider a regression model relating total heat flux to radial deflection for the solar energy data in Table B.2.

a. Suppose that the observed total heat flux is \(250 \mathrm{~kW}\). Find a point estimate of the corresponding radial deflection.
b. Construct a \(90 \%\) confidence interval on radial deflection.

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y X2 X3 X4 271.8 783.35 33.53 40.55 16.66 13.20 264.0 748.45 36.50 36.19 16.46 14.11 238.8 684.45 34.66 37.31 1766 15.68 230.7 827.80 33.13 32.52 1750 10.53 251.6 860.45 35.75 33.71 16.40 11.00 257.9 875.15 34.46 34.14 16.28 11.31 263.9 909.45 34.60 34.85 16.06 11.96 266.5 905.55 35.38 35.89 15.93 12.58 229.1 756.00 35.85 33.53 16.60 10.66 239.3 769.35 35.68 33.79 16.41 10.85 258.0 793.50 35.35 34.72 16.17 11.41 257.6 801.65 35.04 35.22 15.92 11.91 267.3 819.65 34.07 36.50 16.04 12.85 267.0 808.55 32.20 37.60 16.19 13.58 259.6 774.95 34.32 37.89 16.62 14.21 240.4 711.85 31.08 37.71 17.37 15.56 227.2 694.85 35.73 37.00 18.12 15.83 196.0 638.10 34.11 36.76 18.53 16.41 278.7 774.55 34.79 34.62 15.54 13.10 272.3 757.90 35.77 35.40 15.70 13.63 267.4 753.35 36.44 35.96 16.45 14.51 254.5 704.70 37.82 36.26 17.62 15.38 224.7 666.80 35.07 36.34 18.12 16.10 181.5 568.55 35.26 35.90 19.05 16.73 227.5 653.10 35.56 31.84 16.51 10.58 253.6 704.05 35.73 33.16 16.02 11.28 263.0 709.60 36.46 33.83 15.89 11.91 265.8 726.90 36.26 34.89 15.83 12.65 263.8 69715 37.20 36.27 16.71 14.06