1.) Extending the life of an aluminum smelter pot. An investigation of the properties of bricks used to line aluminum smelter pots was published in The American Ceramic Society Bullet (Feb. 2005). Six different commercial bricks were evaluated. The life length of a smelter pot depends on the porosity of the brick lining (the less porosity, the longer the life); consequently, the researchers measured the apparent porosity of each brick specimen, as well as the mean pore diameter of each brick. The data are given in the accompanying table.
Smeltpot
Brick Apparent Porosity (%) Mean Pore Diameter (micrometers)
A 18.8 12.0
B 18.3 9.7
C 16.3 7.3
D 6.9 5.3
E 17.1 10.9
F 20.4 16.8
a.) Find the least squares line relating porosity (y) to mean pore diameter (x).
b.) Interpret the y-intercept of the line.
c.) Interpret the slope of the line.
d.) Predict the apparent porosity percentage for a brick with a mean pore diameter of 10 micrometers.