Excel Definitions

Fitting Polynomials to Data

• Example 8: Let’s try with the Toad Data and a polynomial of degree 3!!!
• Note: The Import Wizard feature that follows only works in MATLAB – for Octave create two vectors, Year and Area with the appropriate toad data as entries – we will see a way to do this in a couple slides!.
• From our class web page, save the toaddata.txt file to your Desktop.
• Within this file, rename the second column Area.
• Next, in MATLAB, from the File menu, choose File-> Import Data and select the toaddata.txt file.
• In the Import Wizard window that appears, click on comma for the Column Separator.
• Click on Next.

Fitting Polynomials to Data

• Example 8 (cont):
• Click on Create vectors from each column using column names.
• Click on Finish.
• Two new vectors have been created – Year and Area.

Fitting Polynomials to Data

• Another way to import data from a text file is via “load”.
• Remove the headings “Year” and “Area” from the first line of the toaddata.txt file.
• Then use the commands
• load(‘toaddata.txt’)
• Year = toaddata(:,1)’
• Area = toaddata(:,2)’

Fitting Polynomials to Data

• Example 8 (cont.)
• Fit our cubic polynomial to the toad data with polyfit:
• p = polyfit(Year, Area, 3)
• To show more decimal places for our coefficients, use
• format long
• Plot the toad data along with the polynomial!
• plot(Year,Area,'r*',Year, polyval(p,Year),'b')
• Compare to Mathematica’s Fit command or Excel’s trendline for a cubic polynomial.
• We should get the same coefficients!

References

• Using MATLAB in Calculus by Gary Jenson