# Question: Example 5 5 described a study of the effectiveness of pomegranate

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)?

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)?

**View Solution:**## Answer to relevant Questions

Example 5.15 described a study that involved substituting sunflower meal for a portion of the usual diet of farm-raised sea breams (Aquaculture [2007]: 528–534). This paper also gave data on y = feed intake (in grams per ...The paper “Developmental and Individual Differences in Pure Numerical Estimation” (Developmental Psychology [2006]: 189–201) describes a study of how young children develop the ability to estimate lengths. Children ...Does high school GPA predict success in first year college English? The proportion with a grade of C or better in freshman English for students with various high school GPAs for freshmen at Cal Poly, San Luis Obispo, in fall ...The following is an excerpt from a letter to the editor written by Roger Cleary that appeared in the San Luis Obispo Tribune (September 16, 2008): The causes of poor fuel economy have nothing to do with higher highway ...The following table gives the number of organ transplants performed in the United States each year from 1990 to 1999 (The Organ Procurement and Transplantation Network, 2003): a. Construct a scatterplot of these data, and ...Post your question