Brick Apparent Porosity (%) Mean Pore Diameter (micrometers) A 18.5 12.0 B 18.3

Question

Brick      Apparent Porosity (%)          Mean Pore Diameter (micrometers)

A       18.5      12.0

B        18.3    9.8

C        16.3   7.3

D       6.9      5.3

E       17.2    10.9

F        20.4     16.8

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. There is not enough information to answer this question.

B. The y-intercept is caret above >0. This value has no meaning because 0 is not in the observed range of the independent variable mean pore diameter.

C. The y-intercept is caret above >0. The mean pore diameter is estimated to be caret above >0 when the apparent porosity is zero.

D. The y-intercept is caret above >0. For each unit increase in mean pore diameter, the mean porosity is estimated to increase by caret above >0 .

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

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

B. The slope of the line is caret above>1. The mean pore diameter is estimated to be caret above >1 when the apparent porosity is zero.

C. There is not enough information to answer this question. The slope of the line is caret above>1. This value has no meaning because 0 is not in the observed range of the independent variable mean pore diameter.

d. Predict the apparent percentage of porosity for a brick with a mean pore diameter of 10 micrometers.

Caret above y= ______% (Round to the nearest thousandth as needed.)

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Porosity %
Independent Variable: Apparent
Porosity % = -0.5508013 + 0.67013123 Apparent
Sample size: 6
R (correlation coefficient) = 0.80413973
R-sq = 0.64664071
Estimate of error standard deviation: 2.6540113

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

a) y = -0.551 + 0.670 x

b) The y-intercept is caret above >0. This value has no meaning because 0 is not in the observed range of the independent variable mean pore diameter. Option B is correct.

c) The slope of the line is caret above >1. For each unit increase in mean pore diameter, the mean porosity is estimated to increase by caret above >1. Option A is correct.

d) For x = 10:

y = 6.151 %

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept -0.5508013 4.1722169 0 4 -0.13201646 0.9013 Slope 0.67013123 0.24768893 0 4 2.7055356 0.0538

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