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3. [15 points] 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 below. Density 0.749 0.798 0.849 0.877 0.929 0.963 0.997 1.046 1.133 1.17 1.215 Dielectric Constant 2.05 2.15 2.25 2.30 2.40 2.47 2.54 2.64 2.85 2.94 3.05 (x₁) Loss Factor (x2) 0.016 0.020 0.022 0.023 0.026 0.028 0.031 0.034 0.039 0.042 0.045 (a) [3 points] Calculate R2 for this model. Interpret this quantity. Round your answer to 4 decimal places. R² = ( Interpretation: (b) [4 points] Construct a normal probability plot of the residuals using RStudio and comment on the normality assumption. Also, show your R code here with a normal probability plot of the residuals. D₁ = ) (c) [8 points] Calculate Cook's distance for the first observation in this data set. Are there any potentially influential observations in these data? Round your answer to 6 decimal places. [e₁/√√8²(1 — h₁₁)] r² h₁1 p (1-₁₁) Interpretation: Р h₁₁ (1-₁₁) )
A 1 Density 2 455 WN 3 6 7 8 9 10 11 12 12 0.749 0.798 0.849 0.877 0.929 0.963 0.997 1.046 1.133 1.17 1.215 B Constant 2.05 2.15 2.25 2.3 2.4 2.47 2.54 2.64 2.85 2.94 3.05 с Factor 0.016 0.02 0.022 0.023 0.026 0.028 0.031 0.034 0.039 0.042 0.045
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