Example 5.5 described a study of the effectiveness of pomegranate fruit extract (PFE) in slowing the growth of prostate cancer tumors (Proceedings of the National Academy of Sciences [October 11, 2005]: 14813€“14818]. Figure 5.11 from that example is reproduced here. Based on this figure, we noted that for the .2% PFE group, the relationship between average tumor volume and number of days after injection of cancer cells appears curved rather than linear.

Apa. One transformation that might result in a relationship that is more nearly linear is log(y). The values of x = number of days since injection of cancer cells, y = average tumor volume (in mm3), and y = log(y) for the 0.2% PFE group are given in the accompanying table. Construct a scatterplot of y versus x. Does this scatterplot look more nearly linear than the plot of the original data?

b. Based on the accompanying Minitab output, does the least-squares line effectively summarize the relationship between y_ and x? The regression equation is

c. Use the Minitab output to predict average tumor size 30 days after injection of cancer cells for a mouse that received water supplemented with 0.2% PFE.
d. Residual plots of the residuals from the least-squares line using the untransformed data and using y and x are shown at the bottom of the page in Figure EX5.44. What feature of the residual plot for the original data suggests that the least-squares line is not the best way to describe the relationship between y and x? In what way does the residual plot for the transformed data suggest that a line is a reasonable description of the relationship for the transformed data (y and x)?

Transcribed Image Text:

Variable e Water average tumor size .2% PFE average tumor size 800 700 u 600 ZI :500 400 300 200 100 0 10 5 20 25 30 35 40 Days after injection Days After Injection 0.2% PFE Average Tumor Size Log(y 1.60 1.88 1.95 2.32 2.36 2.52 2.65 2.78 40 19 23 330 39 log(average tumor size) 1.230.0413 Days After Injection Predictor Constant Days After Injection 0.041250 0.003000 13.75 0.000 S 0.0777817 R-Sq 96.9% R-Sq(adj)-96.4% Coef SE Coef T P 1.22625 0.07989 5 0.000