Statistics for Engineers and Scientists (Looseleaf)
4th Edition
ISBN: 9780073515687
Author: Navidi
Publisher: MCG
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Textbook Question
Chapter 7.4, Problem 14E
The article “Characteristics and Trends of River Discharge into Hudson, James, and Ungava Bays, 1964–2000” (S. Déry, M. Stieglitz, et al., Journal of Climate, 2005:2540–2557) presents measurements of discharge rate x (in km3/yr) and peak flow y (in m3/s) for 42 rivers that drain into the Hudson, James, and Ungava Bays. The data are shown in the following table:
- a. Compute the least-squares line for predicting y from x. Make a plot of residuals versus fitted values.
- b. Compute the least-squares line for predicting y from ln x. Make a plot of residuals versus fitted values.
- c. Compute the least-squares line for predicting ln y from ln x. Make a plot of residuals versus fitted values.
- d. Which of the three models (a) through (c) fits best? Explain.
- e. Using the best model, predict the peak flow when the discharge is 50.0 km3/yr.
- f. Using the best model, find a 95% prediction interval for the peak flow when the discharge is 50.0 km3/yr.
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Students have asked these similar questions
The article "Characteristics and Trends of River Discharge into Hudson, James, and Ungava
Bays, 1964-2000" (S. Dery, M. Stieglitz, et al., Journal of Climate, 2005:2540-2557)
presents measurements of discharge rate x (in kmlyr) andpeakflow y (in m/s) for 42 rivers
that drain into the Hudson, James, and Ungava Bays. The data are shown in the following
table:
Discharge
Peak Flow
94.24
4110.3
66.57
4961.7
59.79
10275.5
48.52
6616.9
40.00
7459.5
32.30
2784.4
31.20
3266.7
30.69
4368.7
26.65
1328.5
22.75
4437.6
21.20
1983.0
20.57
1320.1
19.77
1735.7
18.62
1944.1
17.96
3420.2
17.84
2655.3
16.06
3470.3
1561.6
14.69
11.63
869.8
11.19
936.8
11.08
1315.7
10.92
1727.1
9.94
768.1
7.86
483.3
An article in the Journal of Environmental Engineering (1989, Vol. 115(3), pp.
608–619) reported the results of a study on the occurrence of sodium and chloride in surface
streams in central Rhode Island. The following data are chloride concentration y (in milligrams per
liter) and roadway area in the watershed x (in percentage).
An article in Air and Waste ("Update on Ozone Trends in California's South Coast Air Basin," Vol. 43, 1993) studied the ozone levels
on the South Coast air basin of California for the years 1976-1991. The author believes that the number of days that the ozone
exceeds 0.20 parts per million depends on the seasonal meteorological index (the seasonal average 850 millibar temperature). The
data follow:
Year Days Index
16.3
1976 91
1977 105 17.1
1978 106 18.2
1979 108 18.1
1980 88
17.2
1981 91
18.2
1982 58
16.0
1983 82 17.2
Round your answers to 2 decimal places.
(a) Fit a simple linear regression model to the data. Test for significance of regression using a = 0.05.
y = i
Calculate fo: i
Year Days Index
1984 82
17.7
1985 65
17.2
1986 61
16.9
1987
48
17.1
1988 61
18.2
1989 43 17.3
1990 33 17.5
1991 36
16.6
i
+ i
Is the simple linear regression model significant? No.
(b) Calculate a 95% confidence interval on the slope.
≤B₁ ≤i
X
Chapter 7 Solutions
Statistics for Engineers and Scientists (Looseleaf)
Ch. 7.1 - Compute the correlation coefficient for the...Ch. 7.1 - For each of the following data sets, explain why...Ch. 7.1 - For each of the following scatterplots, state...Ch. 7.1 - True or false, and explain briefly: a. If the...Ch. 7.1 - In a study of ground motion caused by earthquakes,...Ch. 7.1 - A chemical engineer is studying the effect of...Ch. 7.1 - Another chemical engineer is studying the same...Ch. 7.1 - Tire pressure (in kPa) was measured for the right...Ch. 7.1 - Prob. 10ECh. 7.1 - The article Drift in Posturography Systems...
Ch. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - A scatterplot contains four points: (2, 2), (1,...Ch. 7.2 - Each month for several months, the average...Ch. 7.2 - In a study of the relationship between the Brinell...Ch. 7.2 - A least-squares line is fit to a set of points. If...Ch. 7.2 - Prob. 4ECh. 7.2 - In Galtons height data (Figure 7.1, in Section...Ch. 7.2 - In a study relating the degree of warping, in mm....Ch. 7.2 - Moisture content in percent by volume (x) and...Ch. 7.2 - The following table presents shear strengths (in...Ch. 7.2 - Structural engineers use wireless sensor networks...Ch. 7.2 - The article Effect of Environmental Factors on...Ch. 7.2 - An agricultural scientist planted alfalfa on...Ch. 7.2 - Curing times in days (x) and compressive strengths...Ch. 7.2 - Prob. 13ECh. 7.2 - An engineer wants to predict the value for y when...Ch. 7.2 - A simple random sample of 100 men aged 2534...Ch. 7.2 - Prob. 16ECh. 7.3 - A chemical reaction is run 12 times, and the...Ch. 7.3 - Structural engineers use wireless sensor networks...Ch. 7.3 - Prob. 3ECh. 7.3 - Prob. 4ECh. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - The coefficient of absorption (COA) for a clay...Ch. 7.3 - Prob. 8ECh. 7.3 - Prob. 9ECh. 7.3 - Three engineers are independently estimating the...Ch. 7.3 - In the skin permeability example (Example 7.17)...Ch. 7.3 - Prob. 12ECh. 7.3 - In a study of copper bars, the relationship...Ch. 7.3 - Prob. 14ECh. 7.3 - In the following MINITAB output, some of the...Ch. 7.3 - Prob. 16ECh. 7.3 - In order to increase the production of gas wells,...Ch. 7.4 - The following output (from MINITAB) is for the...Ch. 7.4 - The processing of raw coal involves washing, in...Ch. 7.4 - To determine the effect of temperature on the...Ch. 7.4 - The depth of wetting of a soil is the depth to...Ch. 7.4 - Good forecasting and control of preconstruction...Ch. 7.4 - The article Drift in Posturography Systems...Ch. 7.4 - Prob. 7ECh. 7.4 - Prob. 8ECh. 7.4 - A windmill is used to generate direct current....Ch. 7.4 - Two radon detectors were placed in different...Ch. 7.4 - Prob. 11ECh. 7.4 - The article The Selection of Yeast Strains for the...Ch. 7.4 - Prob. 13ECh. 7.4 - The article Characteristics and Trends of River...Ch. 7.4 - Prob. 15ECh. 7.4 - The article Mechanistic-Empirical Design of...Ch. 7.4 - An engineer wants to determine the spring constant...Ch. 7 - The BeerLambert law relates the absorbance A of a...Ch. 7 - Prob. 2SECh. 7 - Prob. 3SECh. 7 - Refer to Exercise 3. a. Plot the residuals versus...Ch. 7 - Prob. 5SECh. 7 - The article Experimental Measurement of Radiative...Ch. 7 - Prob. 7SECh. 7 - Prob. 8SECh. 7 - Prob. 9SECh. 7 - Prob. 10SECh. 7 - The article Estimating Population Abundance in...Ch. 7 - A materials scientist is experimenting with a new...Ch. 7 - Monitoring the yield of a particular chemical...Ch. 7 - Prob. 14SECh. 7 - Refer to Exercise 14. Someone wants to compute a...Ch. 7 - Prob. 16SECh. 7 - Prob. 17SECh. 7 - Prob. 18SECh. 7 - Prob. 19SECh. 7 - Use Equation (7.34) (page 545) to show that 1=1.Ch. 7 - Use Equation (7.35) (page 545) to show that 0=0.Ch. 7 - Prob. 22SECh. 7 - Use Equation (7.35) (page 545) to derive the...
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