Question

An investigation of the properties of bricks used to line aluminum smelter pots was published in an article. Six different commercial bricks were evaluated. The life span of a smelter pot depends on the porosity of the brick lining​ (the less​ porosity, the longer the life​ span); consequently, the researchers measured the apparent porosity of each brick​ specimen, as well as the mean pore diameter of each brick. See the table.

Brick	Apparent Porosity​ (%)	Mean Pore Diameter ​(micrometers)
A	18.6	12.01
B	18.3	9.8
C	16.3	7.37
D	6.9	5.2
E	17.1	10.9
F	20.4	16.81

a. Find the least squares line relating porosity​ (y) to mean pore diameter​ (x).

y=_______+______x​(Round to the nearest thousandth as​ needed.)

b. Interpret the​ y-intercept of the line. Choose the correct answer below.

A.The​ y-intercept is β0. The mean pore diameter is estimated to be β0 when the apparent porosity is zero.

B.There is not enough information to answer this question.

C.The​ y-intercept is β0. This value has no meaning because 0 is not in the observed range of the independent variable mean pore diameter.

D.The​ y-intercept is β0. For each unit increase in mean pore​ diameter, the mean porosity is estimated to increase by β0.

c. Interpret the slope of the line. Choose the correct answer below.

A.The slope of the line is β1.This value has no meaning because 0 is not in the observed range of the independent variable mean pore diameter.

B.The slope of the line is β1. For each unit increase in mean pore​ diameter, the mean porosity is estimated to increase by β1.

C.The slope of the line is β1. The mean pore diameter is estimated to be β1 when the apparent porosity is zero.

D.There is not enough information to answer this question.

d. Predict the apparent percentage of porosity for a brick with a mean pore diameter of 10 micrometers. y=_________% ​(Round to the nearest thousandth as​ needed.)

Answer 1

(a)

X	Y	XY	X2
12.01	18.6	223.386	144.2401
9.8	18.3	179.34	96.04
7.37	16.3	120.131	54.3169
5.2	6.9	35.88	27.04
10.9	17.1	186.39	118.81
16.81	20.4	342.924	282.5761
Total = 62.09	97.6	1088.051	723.0231

So,

the least square line is:

(b)

Correct option:

A. The y - intercept is 0. The mean pore diameter is estimated to be 0 when the apparent porosity is zero.

(c)

Correct option:

B.   The slope of the line is 1. For each unit increase in mean pore diameter, the mean porosity is estimated to increase by 1.

(d)

For x = 10:

So,

Answer is:

15.932%