Fitting Tips

Why use curve fitting tools?

When properly used, curve fitting tools (like Excel's trendline tool) explain the relationship between two variables on a graph. The purpose behind using fitting tools is to give you a deeper understanding of the science behind a graph.

Good fitting starts with a good graph

Since curve fitting is based on a graph, having a high quality graph is essential to using curve fitting tools sensibly. Before you attempt to use a trendline tool, it is essential that you

•  Make sure the two variables you are graphing are truly related. If the two quantities you are graphing are not related, curve fitting will yield meaningless equations.
•  Make sure your graph has at least five or six points. The more data you have, the more confident you can be that the fit is the actual equation that describes the relationship between the two variables in your graph.

Simplicity is the key

In life, the simplest explanation is often the best. This is especially true in curve fitting. Will a straight line best indicate the trend in the data points? What about a power law? An exponential? In general, the fewer numbers in the trendline equation, the better. While it is possible that a third or fourth order polynomial will fit your data, there is often a much simpler equation that fits the data. Remember that the purpose behind curve fitting is to find a simple explanation for the relationship in your data.

Map a strategy before you start

•  Will one equation fit the entire graph? If the shape of your graph changes in the middle, you may need to find more than one trendline equation (see example below). If you decide to use more than one trendline, you will need to explain why the relationship between the variables changes.
•  Does a horizontal line fit the data well? If so, you don't need to use curve fitting tools. Simply draw a horizontal line on the graph to indicate that the y-variable is constant.
•  Is the graph linear? If not, you'll need to try something more complex. Two simple possibilities are power law and exponential. Avoid using complicated polynomial fits.
•  Is there an outlying data point? Sometimes a single data point does not fit in with the rest of the data. Ideally, you should go back to the apparatus to check whether the outlier is a valid and reproducible data point or just due to some mistake. Do not include outliers in your fit unless you are absolutely sure the data point is correct..

Let Excel do all the work

1. Make two columns in Excel. The first column is the independent data (x-axis); the second column is the dependent data (y-axis). (Use a third column to record your raw data and calculate the dependent data using Excel, if necessary.)
2. Make a scatter graph of the y-data vs. the x-data.
3. Click on one of the data points in your graph.
4. On the Chart menu, click Add Trendline.
5. Under Type, choose an appropriate Trend/Regression type.
6. Under Options, click "Display equation on chart".
7. Click "OK".

If Excel places the graph in a location at which it can't be read, click once on the equation. Then place the cursor on the gray boundary surrounding the equation and click-drag it to another location.

Interpret the fit equation

Once you have the fit equation, the hard work begins. Slopes, y-intercepts and other numbers in the fit equations are often connected to actual physical quantities (like velocity, or acceleration, or electric charge). Interpreting the fit equation means explaining the physics behind the equation (and the graph).