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2.5.10: Linear Least Squares Analysis

  • Page ID
    370505
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    To fit a straight line, y = mx + b, to a set of experimentally determined points

    (x 1,y 1), (x 2,y 2), ..., (x n,y n) contained in the vectors [x] and [y], use Basic Fitting under the Tools menu in your graph window. Try this using the following data:

    x = [-3.8 -1.2 0.75 3.1 5.6 8];
    y = [8.2 6 3.3 1.6 -2 -6];
    

    Selecting Basic Fitting from the Tools menu opens up an options box. Select linear as the fit type and choose how many significant figure you want in the calculation. A Linear Least-Squares line will be placed on the graph along with the equation for the line.

    Screen Shot 2022-03-10 at 1.55.54 PM.png
    Figure \(\PageIndex{1}\): Basic Linear Fit. (CC-NC-BY-DUKE CHEM)

    NOTE: Often for our purposes in the Physical Chemistry Laboratory it is often important to know the uncertainties (or standard deviation) in the calculated slope and intercept. To obtain calculated values of the slope, intercept, correlation coefficient along with the uncertainties in slope and intercept, use the lsq command. Using the current x,y data as an example, typing:

    lsq(x,y)

    returns the following:

    Screenshot_3
    Figure \(\PageIndex{2}\): The lsq Function. (CC-NC-BY-DUKE CHEM)

    To perform a weighted linear least-squares analysis, you would use the command wtlsq(x,y). This requires that you enter a weighting factor e.


    2.5.10: Linear Least Squares Analysis is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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