An article in IEEE Transactions on Instrumentation and Measurement (2001, Vol. 50, pp. 2033€“2040) reported on a study that had analyzed powdered mixtures of coal and limestone for permittivity. The errors in the density measurement was the response. The data are reported in Table E12-9.

(a) Fit a multiple linear regression model to these data with the density as the response.

(b) Estimate σ² and the standard errors of the regression coefficients.

(c) Use the model to predict the density when the dielectric constant is 2.5 and the loss factor is 0.03.

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Density Dielectric Constant Loss Factor 0.749 2.05 0.016 0.798 2.15 0.02 0.849 2.25 0.022 0.877 2.3 0.023 0.026 0.929 2.4 0.963 2.47 0.028 0.997 1.046 2.54 0.031 2.64 0.034 1.133 2.85 0.039 1.17 2.94 0.042 0.045 1.215 3.05