Show that the differences in BIC values given in the first column of Table 22.1 (page 680) correspond roughly to the Bayes factors and posterior model probabilities given in columns 2 and 3 of the...

Show that the differences in BIC values given in the first column of Table 22.1 (page 680) correspond roughly to the Bayes factors and posterior model probabilities given in columns 2 and 3 of the table.

Perform model selection for the baseball salary regression using a criterion or criteria different from the BIC, examining the ‘‘best’’ model of each size, and the ‘‘best’’ 10 or 15 models regardless of size. Are the models similar to those nominated by the BIC? Why did you obtain these results?