How to do a POLYNOMIAL FIT to your data
There are 2 Xess functions you will want to use to do this, polyfit and
polycoef.
Take, for example, the following data:
A B C E F
-------------------------------------------------
1 | 1 1
2 | 2 2.1
3 | 3 2.9
4 | 4 4.1
5 | 5 4.9
6 | 6 6.2
7 | 7 6.9
To do a least squares fit, you will want to move the cursor to an
adjacent vacant column (e.g. C1) and enter the following command,
@polyfit(A1..A7,B1..B7,1)
The first range is the "x" data and the second range is the "y" data. The
last number indicates the degree of the polynomial (1 for linear, 2 for
quadratic, etc.). The polyfit command will then generate the y values
corresponding to the type of polynomial fit you desire.
To get the coefficients of the fit, go to another unoccupied cell (e.g.
E1) and enter the following,
@polycoef(A1..A7,B1..B7,1)
Your spreadsheet now will look like,
A B C E F
-------------------------------------------------
1 | 1 1 1.025 0.99642
2 | 2 2.1 2.02142 0.02857
3 | 3 2.9 3.01785
4 | 4 4.1 4.01428
5 | 5 4.9 5.01071
6 | 6 6.2 6.00714
7 | 7 6.9 7.00357
Column C contains the y values of the fitted data points, and column E
contains the coefficients of the fitted polynomial in descending order;
in a linear fit, these correspond to the slope and intercept of the line.
To plot this, you would select "graph", then "New Graph", then the type of
graph you want (in this case, "Line Graph"). Now you need to select your
data ranges. Go to the graphics window and select "Edit" then "Data Sets".
Click in the X Range and enter the data range for the x data (you can also
just highlight the data range and click on the middle mouse in the
appropriate box and the range will appear), then click in the Y Range and
enter the range for your y data. Then you want to select "Line Style" = "No
Line" so only data points are shown. Now, to display the fitted curve, go
to "Edit", "Data Sets", then drag the drag bar to go to data set 2. Enter
new X-range (same as the old X-range), and the Y-range corresponding to the
fitted data (Column C). Select "Line Style" = "Solid", then "Apply". You
should have a graph with data points and a fitted line through them. If you
want to get a little more sophisticated and display the coefficients on the
graph, goto "Options" in the Graph Editor, select "General" and click in the
"Legend" box to enable legends. Then, "Edit", "Data Sets" and enter in the
"Legend" text box,
0.996x+0.029
and "Apply".
Experiment to get the graph looking the way you want.
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