Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 12.2, Problem 18E
For the past decade, rubber powder has been used in asphalt cement to improve performance. The article “Experimental Study of Recycled Rubber-Filled High-Strength Concrete” (Magazine of Concrete Res., 2009: 549–556) includes a regression of y = axial strength (MPa) on x = cube strength (MPa) based on the following sample data:
| x | 112.3 | 97.0 | 92.7 | 86.0 | 102.0 | 99.2 | 95.8 | 103.5 | 89.0 | 86.7 |
| y | 75.0 | 71.0 | 57.7 | 48.7 | 74.3 | 73.3 | 68.0 | 59.3 | 57.8 | 48.5 |
- a. Obtain the equation of the least squares line, and interpret its slope.
- b. Calculate and interpret the coefficient of determination.
- c. Calculate and interpret an estimate of the error standard deviation σ in the simnle linear repression model.
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The accompanying data resulted from an experiment in which weld diameter and shear strength (in pounds) were determined for five different spot welds on steel.
Below are the data collected and the regression equation.
Diameter
Strength
200.1
813.7
210.1
785.3
220.1
960.4
230.1
1118.0
240.0
1076.2
Strength = -941.6992 + 8.5988*Diameter
a)The predicted y-hat value for a diameter of 201 is 864. Interpret this predicted value.
b)what is the predicted strength of a weld with a diameter of 51?
a, b, and c
For the past decade, rubber powder has been used in asphalt cement to improve performance. An article includes a regression of y = axial strength (MPa) on x cube strength (MPa)
based on the following sample data:
112.3 97.0 92.7 86.0 102.0 99.2 95.8 103.5 89.0 86.7
74.7 70.7 58.0 49.2 74.3 73.0 68.3 59.5 57.3 48.9
(a) Obtain the equation of the least squares line. (Round all numerical values to four decimal places.)
%3D
Interpret the slope.
A one MPa decrease in axial strength is associated with an increase in the predicted cube strength equal to the slope.
A one MPa decrease in cube strength is associated with an increase in the predicted axial strength equal to the slope.
A one MPa increase in axial strength is associated with an increase in the predicted cube strength equal to the slope.
A one MPa increase in cube strength is associated with an increase in the predicted axial strength equal to the slope.
(b) Calculate the coefficient of determination. (Round your answer to four…
Chapter 12 Solutions
Probability and Statistics for Engineering and the Sciences
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