11.42 More on predicting bone formation. Now consider a regression model for predicting VO+ using OC, TRAP, and VO−.

  1. (a) Write out the statistical model for this analysis including all assumptions.

  2. (b) Run the multiple regression to predict VO+ using OC, TRAP, and VO−. Summarize the results.

  3. (c) Make a table giving the estimated regression coefficients, standard errors, and t statistics with P-values for this analysis and for the two that you ran in the previous exercise. Describe how the coefficients and the P-values differ for the three analyses.

  4. (d) Give the percent of variation in VO+ explained by each of the three models and the estimate of σ. Give a short summary.

  5. (e) The results you found in part (b) suggest another model. Run that model, summarize the results, and compare them with the results in part (b).