This web page allows users to create scatter plots and, optionally, linear regression parameters for any user-selected pair of parameters of the COHOWeb data set. That is, users may obtain an equation of the form Y = aX + b, where Y and X are user selected from the list of spacecraft specific parameters.

Users specify a time span and time resolution over which to do the analysis. Users may choose to exclude from the analysis any points for which Y values and/or X values lie outside user-specified range(s). In fact, users can exclude points for which any parameter(s) lie outside user-specified range(s). Update added November 2009. Until now, the scatter plots and regression fits enabled by this interface were for concurrent data. The descriptor of the basic functionality follows this Update marked by ******'s.

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We have just added functionalities to perform regression fits and scatter plots where the Y variable is time-lagged relative to the X variable by a single lag of the duration of N data points, and to compute auto- and cross-correlation coefficients for (X,X) or (Y,X) for multiple lags from zero to Nmax. Referring to a step size M and an Nmax, correlation coefficients will be computed for lags of 0, M, 2M, 3M, ..., N* where N* is [M * Integer (Nmax/M)]. Thus if Nmax is 7 and M is 2, correlation coefficients will be computed for lags of 0, 2, 4, 6 data points. Currently, one must use N (or Nmax for multiple lag case) between zero (the no-lag case) and 60. Likewise one must use M such that the number of correlation coefficients computed (including lag = 0) is 11 or less. This means M > Int [(Nmax-1)/10], or equivalently N/M <= 10.

Owing to the lack of ambiguity between the single-lag case and the multiple-lag case, we use in the interface just "N" to mean N for the single lag case and to mean Nmax for the multiple lag case.

Users must first specify a value of N, then specify whether they want (a) full analysis (scatter plot, regression fit, correlation coefficient) for a single lag or (b) merely a listing of points selected for single-lag analysis or (c) correlation coefficients for multiple lags. Also, for the multiple-lag case, a value of M needs to be specified.

In doing filtering, discussed below, parameter values are all considered at the time of the X variable, except for Y itself which is considered at the lagged time.
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Users must specify on the interface which parameters are Y and X, and can exclude points based on ranges of these or any other parameters simply by specifying low and/or high values on the interface line(s) for that (those) parameter(s).

Users may also choose between linear regression methods. The "delta-Y" method determines a and b by minimizing the sum of squares of (Y(observed) - Y(fit)); this is typically used in regression analyses when the likely errors in the Y parameter significantly exceed those in the X parameter. On the other hand the "perpdist" method equivalently minimizes the squares of perpendicular distances between observed (Y,X) points and the best fit line.

Note that analyses are limited to 30,000 points when using the delta-Y method and to 12,000 points when using the perpdist method. These limits do not apply to runs involving no regression analysis (i.e. scatter plots only).

As a separate functionality, the user may "retrieve" all the points which were selected for the scatter plot and regression fit calculation, or may retrieve points independent of doing a scatter plot and fit. This latter capability is an enhancement to the basic COHOWeb data retrieval functionality in that it allows filtering by values of selected or other parameters for each of spacecraft.

References:
Delta-Y method:
Program - CORRELATE.PRO from:
Research Systems, Inc., Interactive Data Language, Version 5.3

Perpdist method:
Program - fitexy.for from:
Chapter 15.3 in: Press, W. H., S. A. Teukolsky, W. T. Vetterling, 
and B. P. Flannery,
Numerical recipes in FORTRAN, Second Edition, Cambridge
University Press,
New York, 963 pp., 1992.

If you have any questions/comments about COHOWEB system, contact: Dr. Natalia Papitashvili, Mail Code 672, NASA/Goddard Space Flight Center, Greenbelt, MD 20771

Last Update: October 1, 2004, NEP.
NASA Official: Robert Candey (Robert.M.Candey@nasa.gov), Head of the Space Physics Data Facility