biomark

11.43 Predicting bone formation using transformed variables. Because the distributions of VO+, VO−, OC, and TRAP tend to be skewed, it is common to work with logarithms rather than the measured values. Using the questions in the previous three exercises as a guide, analyze the log data.

11.43 All variables are Normal when log transformed. All pairs are positively associated: strongest between LVO + and LVO − (r = 0.8396) and weakest between LOC and LVO − (r = 0.5545). Using logOC: $\hat{y}$ = 4.39 + 0.71logOC, t = 6.57, P < 0.0001, R² = 59.83%, s = 0.36. Using logOC and logTRAP: $\hat{y}$ = 4.26 + 0.43logOC + 0.42logTRAP, t = 2.56, P = 0.0162, t = 2.06, P = 0.0484, R² = 65.14%, s = 0.34. Using all three: $\hat{y}$ = 0.87 + 0.39logOC + 0.03logTRAP + 0.67logVO − , t = 3.40, P = 0.0021, t = 0.17, P = 0.8624, t = 5.71, P < 0.0001, R² = 84.21%, s = 0.23. The best model uses only logOC and logVO − : $\hat{y}$ = 0.83298 + 0.40589logOC + 0.68159logVO − , R² = 84.19%, s = 0.23.