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Solved: An article in the Journal of the American
Chapter 11, Problem 70E(choose chapter or problem)
An article in the Journal of the American Statistical Association [“Markov 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 \(\alpha=0.05\).
(c) Estimate \(\sigma^{2}\) for this model.
(d) Calculate \(R^{2}\) 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 \(\hat{y}\) and versus x. Does the assumption of constant variance seem to be satisfied?
TABLE.E11-5 Strength Data
\(\begin{array}{|cccc|}
\hline \begin{array}{c}
\text { Compressive } \\
\text { Strength }
\end{array} & \text { Density } & \begin{array}{c}
\text { Compressive } \\
\text { Strength }
\end{array} & \text { Density } \\
\hline 3040 & 29.2 & 3840 & 30.7 \\
2470 & 24.7 & 3800 & 32.7 \\
3610 & 32.3 & 4600 & 32.6 \\
3480 & 31.3 & 1900 & 22.1 \\
3810 & 31.5 & 2530 & 25.3 \\
2330 & 24.5 & 2920 & 30.8 \\
\hline 1800 & 19.9 & 4990 & 38.9 \\
3110 & 27.3 & 1670 & 22.1 \\
\hline 3160 & 27.1 & 3310 & 29.2 \\
\hline 2310 & 24.0 & 3450 & 30.1 \\
\hline 4360 & 33.8 & 3600 & 31.4 \\
1880 & 21.5 & 2850 & 26.7 \\
\hline 3670 & 32.2 & 1590 & 22.1 \\
1740 & 22.5 & 3770 & 30.3 \\
\hline 2250 & 27.5 & 3850 & 32.0 \\
\hline 2650 & 25.6 & 2480 & 23.2 \\
\hline 4970 & 34.5 & 3570 & 30.3 \\
\hline 2620 & 26.2 & 2620 & 29.9 \\
\hline 2900 & 26.7 & 1890 & 20.8 \\
\hline 1670 & 21.1 & 3030 & 33.2 \\
\hline 2540 & 24.1 & 3030 & 28.2 \\
\hline
\end{array}\)
Questions & Answers
QUESTION:
An article in the Journal of the American Statistical Association [“Markov 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 \(\alpha=0.05\).
(c) Estimate \(\sigma^{2}\) for this model.
(d) Calculate \(R^{2}\) 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 \(\hat{y}\) and versus x. Does the assumption of constant variance seem to be satisfied?
TABLE.E11-5 Strength Data
\(\begin{array}{|cccc|}
\hline \begin{array}{c}
\text { Compressive } \\
\text { Strength }
\end{array} & \text { Density } & \begin{array}{c}
\text { Compressive } \\
\text { Strength }
\end{array} & \text { Density } \\
\hline 3040 & 29.2 & 3840 & 30.7 \\
2470 & 24.7 & 3800 & 32.7 \\
3610 & 32.3 & 4600 & 32.6 \\
3480 & 31.3 & 1900 & 22.1 \\
3810 & 31.5 & 2530 & 25.3 \\
2330 & 24.5 & 2920 & 30.8 \\
\hline 1800 & 19.9 & 4990 & 38.9 \\
3110 & 27.3 & 1670 & 22.1 \\
\hline 3160 & 27.1 & 3310 & 29.2 \\
\hline 2310 & 24.0 & 3450 & 30.1 \\
\hline 4360 & 33.8 & 3600 & 31.4 \\
1880 & 21.5 & 2850 & 26.7 \\
\hline 3670 & 32.2 & 1590 & 22.1 \\
1740 & 22.5 & 3770 & 30.3 \\
\hline 2250 & 27.5 & 3850 & 32.0 \\
\hline 2650 & 25.6 & 2480 & 23.2 \\
\hline 4970 & 34.5 & 3570 & 30.3 \\
\hline 2620 & 26.2 & 2620 & 29.9 \\
\hline 2900 & 26.7 & 1890 & 20.8 \\
\hline 1670 & 21.1 & 3030 & 33.2 \\
\hline 2540 & 24.1 & 3030 & 28.2 \\
\hline
\end{array}\)
Step 1 of 7
Given:
Data are given on the compressive strength parallel to the grain versus resin-adjusted density for specimens of radiata pine.