Vernier Logger Pro Modeling, Fitting, and Linearization - Manual (Page 5)

Logger Pro Modeling, Fitting, and Linearization
©Vernier Software & Technology 5
Curve Fitting
Steps
1. Enter or record data in Logger Pro.
2. Insert a graph of the two variables being analyzed (with Connect Points turned off under
Graph Options ). Select the graph.
3. In the Analyze menu choose Curve Fit, then the analytic function you think will match.
4. The coefficients will be calculated for you using a least squares analysis along with the
Root Mean Square Error (RSME).
5. If the match is not good, try picking or entering another function (or repeat the fitting if you
are matching a sine, cosine or tangent function).
6. Close the window with the small graph you matched. This displays a larger overlay graph.
Make more changes on it, if needed.
Pros
1. Fitting usually takes less time than modeling,
2. It provides standard error analysis
Cons
1. Fitting does not help users focus on what shapes various analytic functions have.
2. Fitting does not help users learn how each coefficient in an equation affects the graph of
the analytic function.
3. Sometimes when fitting many cycles of a sinusoidal function, fitting must be repeated
several times to obtain a fit.
4. Envelopes of functions that can be seen visually cannot be fit without creating a new data
set with local maxima or minima. For example the local maxima of a damped oscillation
can be modeled but not fit without a lot of extra work.
Linearization
Steps
1. If theory or the shape of a graph of y vs. x suggests that the equation linking these
variables can be put in the form g(y) = Af(x)+B, then linearization is possible. For example,
if the equation is y = Ax
p where p is a non-zero number, then g(y) = y and f(x) = x p .
2. Enter or record the x, y data in Logger Pro.
3. Use New Calculated Column in Logger Pro to create new variables g(y) and f(x).
4. Plot g(y) versus f(x). If the graph is not linear try finding other functions g(y) and/or f(x). For
example, if f(x) = x p , try another value of p.
5. If the linearized data appear to lie along a line, then choose Linear Fit in the Analyze
menu The coefficients A and B will be calculated for you using a Linear Regression
analysis along with the Root Mean Square Error (RSME).
Pros
1. Many older scientists and teachers are comfortable with it.
2. If a function can be linearized and if no computer is available, then manual calculations and
graphing can be performed more easily than for other methods. In particular, log or log-log
paper might be useful.
3. The uncertainty in the linearized parameter is easy to obtain using a basic least squares
analysis. However, it may be difficult to interpret.
Cons
1. A graph of linearized data is a straight line so the nature of the relationship between the
original variables cannot be visualized.
2. Putting an equation in the form g(y) = Af(x)+B may require a lot of cleverness.
3. Data that matches many interesting functional relationships cannot be easily linearized.
Trigonometric functions, quadratic functions where the coefficient B ≠ 0, and various other
functions cannot be analyzed using linearization.