This web page allows users to create scatter plots and, optionally, linear regression parameters for any user-selected pair of parameters of the hourly or high resolution OMNI 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 OMNI 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 OMNI parameter(s) lie outside user-specified range(s).

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. In its past cross-comparisons of like parameters from multiple data sets contributing to OMNI, NSSDC has used the perpdist method. See References below.

Which method is preferable depends on availability of standard deviations of parameters being analyzed. Note that the only hourly (or daily or 27-day) OMNI parameters having standard deviations included in the OMNI records are IMF magnitude, GSE cartesian components of the IMF and plasma density, flow speed, temperature, flow direction angles and alpha/proton ratio. For High Resolution OMNI, only IMF magnitude has a standard deviation. The delta-Y linear regression routine uses these, when available, as the uncertainties in the Y parameter. The "perpdist" routine uses them, when available, in both the Y and X parameters. When not available, uncertainty = 1.0 is used in these routines. When doing a regression between one parameter having standard deviations and another not having standard deviations, one should use the delta-Y method and should let the parameter having standard deviations be the Y variable. When doing regressions between parameters both having standard deviations, the perpdist method may be preferable. Finally, when doing a regression between parameters neither of which has standard deviations, the user may want to use the delta-Y method twice (y=a+bx and x=a'+b'y, convert the second to y=(-a'/b')+(1/b')x and finally let y=.5*[(a-a'/b') + (b+(1/b'))*x]

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 OMNIWeb data retrieval functionality in that it allows filtering by values of selected or other parameters.

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.