One of the ways cause and effect is better understood is by modeling the behavior with a math equation. To generate a math equation from a collection of data, we will use a process called "linearizing data."
In this physics course there are three types of graphs that our labs data will generate. They are
![Curve types by shape](pics-reading/curveTypes.png)
You need to recognize the graph types by their appearance. Unfortunately, the inverse graphs look similar. The inverse squared form has a curve that bends closer to the origin. Only by linearizing the data would you know that the function is either 1/x or 1/x2.
Line of Best Fit or "Trend line" |
There are a few ways to determine line that best represents a collections of data. We use the least squares method. Below is a collection of data points and the line of best fit.
![](pics-reading/graph v vs t.png)
The line of best fit provides a math model to make predictions about data points not on the graph and to evaluate the math model's precision. This math model yields an equation for a straight line in the form of "y = mx + b." Most programs interpret the data to give you the value for the slope and intercept.
The trendline function is Google Sheets can give you the slope and y-intercept.
There are two ways to evaluate if the y=mx+b that is derived from the line of best fit is close to representing the data.
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The software calculates a value called the Regression coefficient, "R." The closer the absolute value of "R" is to 1, the better the fit of the trendline. |
2 |
Use your brain and look at the data points. The line of best fit should closely follow about 70% or more the data points. |
From the math expression y = mx + b to the "science" equation |
This 94 second video explains how to go from y = mx + b to an equation with the variables we use in science.
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