An article in the Journal of the American Statistical Association [Markov Chain Monte Carlo Methods for Computing

An article in the Journal of the American Statistical Association [€œMarkov Chain Monte Carlo Methods for Computing Bayes Factors: A Comparative Review€ (2001, Vol. 96, pp. 1122€“1132)] analyzed the tabulated data on compressive strength parallel to the grain versus resin-adjusted density for specimens of radiata pine. The data are in Table E11-5.

(a) Fit a regression model relating compressive strength to density.

(b) Test for significance of regression with α = 0.05.

(c) Estimate σ² for this model.

(d) Calculate R² for this model. Provide an interpretation of this quantity.

(e) Prepare a normal probability plot of the residuals and interpret this display.

(f) Plot the residuals versus y and versus x. Does the assumption of constant variance seem to be satisfied?

TABLE 11-5 Strength Data

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Compressive Strength Compressive Strength 3840 Density Density 3040 29.2 30.7 2470 32.7 24.7 3800 32.3 3610 4600 32.6 1900 3480 31.3 22.1 31.5 25.3 3810 2530 24.5 2330 2920 30.8 1800 19.9 4990 38.9 27.3 1670 22.1 3110 3310 3160 27.1 29.2 30.1 2310 24.0 3450 31.4 4360 33.8 3600 2850 1880 21.5 26.7 3670 32.2 22.1 1590 1740 22.5 3770 30.3 2250 3850 27.5 32.0 2480 23.2 2650 25.6 34.5 30.3 4970 3570 26.2 2620 2620 29.9 2900 26.7 1890 20.8 33.2 1670 21.1 3030 3030 2540 24.1 28.2