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]: 1481314818]. 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

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)?