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Once you plot your graph, you’ll spend time comparing models and trendlines.

Chances are that you’ve become fairly good at plotting data and calculating slopes.  For many of your math classes and lab reports up until now, the slope was “THE ANSWER”.

Welcome to a brand new world, future fellow physicists! Let’s go a bit deeper into analyzing data and comparing models and trendlines.

Trendlines and Models

Models are the equations that describe physical situations.  These are the equations that you’ve come to know and love while taking your physics classes. For example, Einstein’s famous equation is a model.

$$E = m c^2$$

The kinematics equation for velocity is also a model.

$$v = v_0 + a (\Delta t)$$

Trendlines are the fits that we add to a graph. We use the trendline equation to compare our fit to the model.

For most introductory physics classes, the model and the trendline follow each other closely.

Sometimes though, we have to play around with the equations to match the trendlines.

Linear Trendlines

If you go into Excel, Google Sheets, or another spreadsheet program, you can add trendlines to graphs you produce. In excel there are several options.

The most common form of trendline is the linear trendline.

The equation for this trendline is the slope intercept form,

$$y = m x + b$$

• y represents the dependent variable,
• m represents the slope.
• x represents the independent variable,
• b represents the y intercept, where the graph crosses the y axis at x equals zero.

The trendline you pick should represent the model you are testing.

Be careful here.  Make sure you know which variable is which. For example, don’t confuse the m for the slope with the m for the mass in the experiment you are doing.

Also be careful when you plot the value of the x-position on the y axis, as you might do on a position vs. time graph.