Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 13.4, Problem 43E
a.
To determine
Find the predicted value for surface area when cobalt is 2.6 and the temperature is 250.
Find its corresponding residual value.
b.
To determine
Whether it is reasonable to interpret that there will be a decrease in the surface area by 46 units if the cobalt content increases by 1 unit by holding other variables constant.
c.
To determine
Identify whether there is a linear relationship between response and the predictors.
d.
To determine
Test the significance of
e.
To determine
Find the 95% confidence interval for the true response when temperature is 500 and the cobalt content is 2.
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Students have asked these similar questions
The article "Permeability, Diffusion and Solubility of Gases" (B. Flaconnèche, et al., Oil
and Gas Science and Technology, 2001:262–278) reported on a study of the effect of
temperature and other factors on gas transport coefficients in semicrystalline polymers. The
permeability coefficient (in 10-6 cm³ (STP) / cm · s· MPa) of CO, was measured for
extruded medium-density polyethylene at both 60°C and 61°C. The results are as follows:
60°C: 54 51 61 67 57 69 60
60 63 62
61°C:
58 60 66 66 68 61 60
Find a 95% confidence interval for the difference in the permeability coefficent between
60°C and 61°C.
5.1 Byers and Williams (Viscosities of Binary and Ternary Mixtures of Polyaromatic
Hydrocarbons," Journal of Chemical and Engineering Data, 32, 349 – 354, 1987)
studied the impact of temperature (the regressor) on the viscosity (the response) of
toluene - tetralin blends. The following table gives the data for blends with a 0.4 molar
fraction of toluene.
+
Temperature (°C)
Viscosity (mPa·s)
1.133
24.9
35.0
0.9772
44.9
0.8532
55.1
0.7550
65.2
0.6723
75.2
0.6021
85.2
0.5420
95.2
0.5074
a. Plot a scatter diagram. Does it seem likely that a straight line model will be adequate?
The cetane number is a critical property in specifying the ignition quality of a fuel used in a
diesel engine. Determination of this number for a biodiesel fuel is expensive and time-
consuming. The article "Relating the Cetane Number of Biodiesel Fuels to Their Fatty Acid
Composition: A Critical Study" (J. of Automobile Engr., 2009: 565–583) included the
following data on x = iodine value (g) and y = cetane number for a sample of 15 biofuels
The iodine value (x) is the amount of iodine necessary to saturate a sample of 100 g of oil.
The article's authors fit the simple linear regression model to this data, so let' s does the
same.
132.0 129.0 120.0 113.2 105.0 92.0 84.0 88.4 59.0 80.0 81.0 81.5 71.0 69.2 63.0
y
46.0
48.0
51.0 52.1
54.0 52.0 59.0 58.7 61.6 64.0 61.4 54.6 58.8 58.0
51.4
Construct a scatter plot for the data. Identify and state which is dependent and
independent variable. What is the purpose of the scatter plot/diagram?
2.
Fit a simple linear regression line/ equation to…
Chapter 13 Solutions
Probability and Statistics for Engineering and the Sciences
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