4. In water-resources engineering, the sizing of reservoirs depends on accurate estimates of water flow in the river that is being impounded. For some rivers, long-term historical records of such flow data are difficult to obtain. In contrast, meteorological data on precipitation are often available for many years past. Therefore, it is often useful to determine a relationship between flow and precipitation. This relationship can then be used to estimate flows for years when only precipitation measurements were made. The following data are available for a river that is to be dammed: Precip., cm/yr 88.9 108.5 104.1 139.7 127 94 116.8 99.1 Flow, m/s 14.6 16.7 15.3 23.2 19.5 16.1 18.1 16.6 a. Fit a straight line to these data and predict the annual water flow if the precipitation is 120 cm. b. Compute the standard deviation, the standard error of the estimate, and the correlation coefficient for the fit. Comment on the fit of the estimate line.
4. In water-resources engineering, the sizing of reservoirs depends on accurate estimates of water flow in the river that is being impounded. For some rivers, long-term historical records of such flow data are difficult to obtain. In contrast, meteorological data on precipitation are often available for many years past. Therefore, it is often useful to determine a relationship between flow and precipitation. This relationship can then be used to estimate flows for years when only precipitation measurements were made. The following data are available for a river that is to be dammed: Precip., cm/yr 88.9 108.5 104.1 139.7 127 94 116.8 99.1 Flow, m/s 14.6 16.7 15.3 23.2 19.5 16.1 18.1 16.6 a. Fit a straight line to these data and predict the annual water flow if the precipitation is 120 cm. b. Compute the standard deviation, the standard error of the estimate, and the correlation coefficient for the fit. Comment on the fit of the estimate line.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:4. In water-resources engineering, the sizing of reservoirs depends on accurate estimates of
water flow in the river that is being impounded. For some rivers, long-term historical records
of such flow data are difficult to obtain. In contrast, meteorological data on precipitation are
often available for many years past. Therefore, it is often useful to determine a relationship
between flow and precipitation. This relationship can then be used to estimate flows for years
when only precipitation measurements were made. The following data are available for a river
that is to be dammed:
Precip.,
cm/yr 88.9 108.5 104.1 139.7 127 94 116.8 99.1
Flow,
m/s 14.6 16.7 15.3 23.2 19.5 16.1 18.1 16.6
a. Fit a straight line to these data and predict the annual water flow if the precipitation is
120 cm.
b. Compute the standard deviation, the standard error of the estimate, and the correlation
coefficient for the fit. Comment on the fit of the estimate line.
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