Curve fit - Regression software
Curve fit/plot Regression software Expression evaluator - Download
Curve fit - Regression software - Introduction
Often, we are faced with the task of finding the relationship
(regression)
between two sets of numbers, so that interpolation and extrapolation
can be done by regression software. Many laboratory experiments are sources for huge amounts
of numbers in which, if possible, should be replaced and
represented by an "easier to read" function. Measurements of physical
properties such as viscosity, density, vapor pressure or thermal
conductivity are examples of such data sources.
If there is enough data information to find the relationship between
X and Y, interpolation and extrapolation is possible. Today this
realtionship is easy to find by the use of computers and regression
software.
The relationship was, in fact in earlier times,
often found by plotting data
on various graphs i.e. linear or log-log to see which one
gave the best fit.
To help determine how good the fit is for
the curve selected, the SSE (Sum of Squares Error) and the
coefficient of fit performance (r2) are reported.
The best fit usually have the smallest SSE
and a coefficient of performance near 1.000.
The curve is automatically refitted anytime Calculate
push button is used or a change in a curve type occurs.
Fitting functions to empirical data are not always a straight forward
procedure. Two functions may have an approximately equal coefficient of
performance. If so, as a rule, the simplest function of these should be selected.
regression definition - the relation between selected
values of x and observed values of y (from which the most probable
value of y can be predicted for any value of x)
Starting a New Data Set - Curve fit
To fit a curve to a new data set, just remove the content (if any)
in Data (X Y) edit field and insert your data.
Numeric data must be separated by one or more spaces.
Examples of legal numbers are: -1.234, -1.234E-4,
1.234, 1.234E4
The Curve Fit tool in CHEMIX allows you to define a data set
title, assign axis titles and select a curve type.
The Edit list box push buttons allows you to save, replace
and delete your X Y data sets.
Loading an Existing Data Set - Curve Fit
To load a previously saved data set, double click one of the
elements in the Name (X Y data) list box. The application
reads the data from a file and displays it in the
Data (X Y) text field.
Saving Data
Once you have entered a data set, enter a data title in the
Name (X Y data) edit field and
save your data using one of the push buttons in the Insert frame
(Before or After) in Edit list box
Function, r2 and SSE - Curve fit
Function: Function in which represent the output curve.
r2 The goodness of the
fit - 1.0 is perfect.
SSE Sum of Squares Error. The sum of
(Yi-Yfunc)2.
Function Plot f(x) - Expression Evaluator
The CHEMIX expression evaluator allows you to insert and plot math functions.
Available functions are described in Calculator.
Enter a function e.g. sin(x) in the Plot function f(x) text field
and Calculate. A plot can now be seen in the plot area.
Derivatives - Expression evaluator and X,Y-Data
You may plot derivatives of both the inserted function and XY-data simply
by selecting one of the radio buttons (Y' or Y'') in the
Derivatives area.
NOTE: Taking derivatives of XY-data will not alter any of the data presented in the XY Data field.
Zoom
Zoom by moving the mouse cursor in plot area while left
mouse button is pressed.
The zoom actually occurs when releasing the mouse button. If you want
to go back to initial XY-max/min values (un-zoom), simply press left
mouse button in the plot area and release without moving the mouse cursor.
Note: If any zoom exceeds factor 1/2000, initial xy-max/min values
(before zoom) will automatically be selected.
Max/Min Limits in a Plot
A built-in feature in CHEMIX uses a set of rules finding
the y-limits in a function plot.
If both XY-data and a function are present,-
it will be the extreme max/min limits of the xy-data in which will
decide these limits. In the case of the presence of function plot only,
y-limits will be calculated automatically and x-limits manually.
Radians & Degrees
A function plot may involve trig.func. as sin(x),cos... You may select
Radians or Degrees (Degrees unselected).
Data Manipulation g(x,y)
It is possible to manipulate inserted or generated XY-data . This can be done
by inserting a function in the Data Manipulation f(x,y) field
an Calculate. None of the raw data seen in the Data XY-field
will be altered during this operation,.. the result can
only be seen graphically as a plot. It is possible to insert both
X and Y.
E.g. Y=Y meaning
Yi (new)=Yi (old)
does not change anything while Y=Y/X
meaning Yi (new)=Yi (old)/Xi
does change all the Y-values in the plot.
All available functions are described in Calculator.
Interpolate (Data X Y)
By selecting Interpolate, lines may be drawn between points. Polyline
draw straight lines between the points. Natural cubic spline
assigns third order polynomes to the points.
Printing
You may send the plotted curve to a printer
by selecting the Print Button
(printer graphic). The hard copy will have the same
format as seen on the screen.
Calculate
Plot the selected curve by the use of the Calculate push button.
This button also automatically calculate max/min limits for the plot,
unless the content in one of the X-min X-max Y-min...
(manual limits) fields
prior to the use of this button has been altered.
NOTE:In some cases when a data set contain "illegal values",
as when the denominator in a hyperbolic function equals zero,
no fit/plot will occur.
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