In a study by the U.S. Forestry Service, the relationship between certain chemical elements and oak tree defoliation was studied. A random sample of oak trees was obtained, and the concentration of...

In a study by the U.S. Forestry Service, the relationship between certain chemical elements and oak tree defoliation was studied. A random sample of oak trees was obtained, and the concentration of phosphorus (x, in g/kg) in leaves was measured for each tree. The percentage of defoliation (y) for each tree was carefully estimated at the end of the growing season.

a. Carefully sketch a scatter plot of these data. Describe the relationship between these two variables.

b. Find the estimated regression line. Is this regression significant? Conduct an appropriate test at the 0.05 level. Add a graph of this line to your scatter plot in part (a).

c. Find the residuals, and sketch a graph of the residuals versus the predictor variable.

d. How could this model be improved? Justify your answer.

In a study of hair regeneration, 30 men over 45 years old who had used minoxidil for six months were randomly selected. The daily dose of minoxidil (x, in mg) and the hair density ( y, in hairs/mm2 ) were recorded for each man. The following summary statistics were reported.