Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
9th Edition
ISBN: 9798214004020
Author: Jay L. Devore
Publisher: Cengage Learning US
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Chapter 12.2, Problem 17E
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 simple 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 regression model to predict Y, the state burglary rate per 100,000 people, used the following four state predictors: X₁ = median age,
X₂ = number of bankruptcies per 1,000 population, X3 = federal expenditures per capita (a leading predictor), and X4 = high school
graduation percentage.
Click here for the Excel Data File
(a) Using the sample size of 50 people, calculate the tcalc and p-value in the table given below. (Negative values should be indicated
by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 4 decimal places.)
Predictor
Intercept
AgeMed
Bankrupt
FedSpend
HSGrad%
Coefficient
t-value =
4,198.5808
-27.3540
17.4893
-0.0124
-29.0314
SE
799.3395
12.5687
12.4033
0.0176
7.1268
tcalc
p-value
(b-1) What is the critical value of Student's t in Appendix D for a two-tailed test at a = .01? (Round your answer to 3 decimal places.)
A regression model to predict Y, the state burglary rate per 100,000 people, used the following four state predictors: X1 = median age,
X2 = number of bankruptcies per 1,000 population, X3 = federal expenditures per capita (a leading predictor), and X4 = high school
graduation percentage.
Click here for the Excel Data File
(a) Using the sample size of 45 people, calculate the tcalc and p-value in the table given below. (Negative values should be indicated
by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your t-values to 3 decimal places and p-
values to 4 decimal places.)
Predictor
Intercept
AgeMed
Coefficient
SE
tcalc
p-value
4,641.0430
798.0634
-28.8630
12.4684
Bankrupt
20.1604
12.1079
FedSpend
HSGrad%
-0.0181
0.0181
-30.3196
7.1136
(b-1) What is the critical value of Student's tin Appendix D for a two-tailed test at a = .01? (Round your answer to 3 decimal places.)
-value =
Chapter 12 Solutions
Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
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