The processing of raw coal involves "washing," in which coal ash (nonorganic, incombustible material) is removed. The article "Quantifying Sampling Preash to the density of a coal particle. The average percentage ash for five densities of coal particles was measured. The data are presented in the following table:

Density (g/cm3 )            Percent ash

1.25                                 1.93

1.325                               4.63

1.375                               8.95

1.45                               15.05

1.55                               23.31

a. Construct a scatterplot of percent ash (y) versus density (x).

b. Compute the least-squares line for predicting percent ash from density.

c. If two coal particles differed in density by 0.1 g/cm3 , by how much would you predict their percent ash to differ?

d. Predict the percent ash for particles with density 1.40 g/cm3 .

e. Compute the fitted values.

f. Compute the residuals. Which point has the residual with the largest magnitude?

g. Compute the correlation between density and percent ash.