My WebLink
|
Help
|
About
|
Sign Out
Home
Browse
Search
FLOOD01900
CWCB
>
Floodplain Documents
>
Backfile
>
1001-2000
>
FLOOD01900
Metadata
Thumbnails
Annotations
Entry Properties
Last modified
11/23/2009 10:40:54 AM
Creation date
10/4/2006 10:26:47 PM
Metadata
Fields
Template:
Floodplain Documents
County
Statewide
Community
Nationwide
Title
Techniques of Weather-Resources Investigations of the USGS Book 4, Chapter A1
Date
1/1/1968
Floodplain - Doc Type
Educational/Technical/Reference Information
There are no annotations on this page.
Document management portal powered by Laserfiche WebLink 9 © 1998-2015
Laserfiche.
All rights reserved.
/
44
PDF
Print
Pages to print
Enter page numbers and/or page ranges separated by commas. For example, 1,3,5-12.
After downloading, print the document using a PDF reader (e.g. Adobe Reader).
Show annotations
View images
View plain text
<br />. <br /> <br />SOME STATISTICAL TOOLS IN HYDROLOGY <br /> <br />9 <br /> <br />This manual emphasizes regression over <br />correlation, not only because correlation is <br />commonly inapplicable to particular hydrologic <br />data but because regression provides quantita- <br />tive answers to specific problems. In general, <br />regression is preferred over correlation for <br />hydrologic problems even when the data are <br />suitable for a correlation analysis. Uses of <br />regression analysis are: <br /> <br />1. To estimate individual values of the de- <br />pendent variable corresponding to selecte d <br />values of the independent variables. <br />2. To determine the amount of change in the <br />dependent variable associated with a unit <br />change in an independent variable. <br />3. To determine whether certain variables <br />(which do not have probability distribu- <br />tions) are related to a dependent variable. <br />4. To improve estimates of the parameters <br />defining the probability distribution of the <br />dependent variable. <br /> <br />Correlation is most useful in theoretical <br />studies and in time-series analysis. <br /> <br />. <br /> <br />Serial correlation <br /> <br />. <br /> <br />It has been pointed out that for a probability <br />distribution to be valid the individuals must <br />occur randomly or be drawn randomly. Hydro- <br />logic data such as daily stream discharges form <br />a time series, that is, a sequence of values <br />arranged in order of occurrence. The character- <br />istics and analysis of hydrologic time series <br />have been described by Dawdy and Matalas <br />(1964). A common characteristic of a time <br />series is the existence of a nonrandom element <br />which produces a dependence between observa- <br />tions k units apart. This dependence is called <br />serial correlation, and its degree is measured <br />by the serial correlation coefficient. <br />First-order serial correlation is the depend- <br />ence between observations adjacent in time; <br />the kth order is the dependence between <br />observations k units apart. A plot of the serial <br />correlation coefficient against order is a correlo- <br />gram (Dawdy and Matalas, 1964). <br />To determine the serial correlation, the time <br />series is related to itself offset k units. For <br />example, the time series in the first column <br />below is related to itself shifted one observation <br /> <br />to obtain the first-order serial correlation <br />coefficient. <br /> <br />Xl <br />X, Xl <br />X, X, <br /> <br />Xn xn-l <br /> <br />Computational details are the same as for the <br />relation between two variables and are given <br />in the section on "Simple Linear Regression." <br />A test of significance of a first-order serial <br />correlation coefficient is given by Dawdy and <br />Matalas (1964). <br /> <br />Regression Methods <br /> <br />The previous section described regression <br />in general terms and concluded with some uses <br />of regression. This section describes the compu- <br />tation and interpretation of regression equations, <br />both analytical and graphical, and some char- <br />acteristics of the regression method. <br /> <br />Regression models <br /> <br />We begin a regression problem with a de- <br />pendent variable which we want to predict <br />from one or more independent variables. The <br />independent variables are values or character- <br />istics which seem to be physically related to the <br />dependent variable. Next we need a model <br />which describes the way in which the inde- <br />pendent variables are related to the dependent <br />variable. The model should be in accord with <br />known physical principles, but its exact form <br />may be dictated by the data used. <br />Using a dependent variable, Y, and inde- <br />pendent variables, X and Z, the equations and <br />graphs of some more common regression models <br />are shown in figure 10. Joint relations, those <br />which include a variable which is the product <br />of two other variables, have been discussed in <br />detail by Ezekiel and Fox (1959). The product <br />of two variables is called an interaction term. <br />Combinations of the models shown in figure <br />10 can be used to describe more complicated <br />relations, and the equations can be readily <br />
The URL can be used to link to this page
Your browser does not support the video tag.