Curve Fitting

After plotting data to a scatter plot, it is useful to fit a line or curve that approximately represents the data. For example, if all the data points are roughly in a line, you could draw a straight line through them. If the points are in a curved shape, like a parabola, you would draw a parabola through them.

It is always easier to fit a straight line to a graph. Therefore, the scales of a graph are sometimes modified so that a curved graph is transformed into a line.

The least squares method is most often used to fit data to a line. The main idea of the least squares method is to minimize the vertical distance between each point and the line. When data is roughly in a linear, people usually have no trouble fitting the appropriate line to the data.

Once you have a line fitted to your data, you can use the line to extrapolate more data from the graph. It is easy to determine the equation of a line. The equation you determine is a function that relates the quantities on the graph.

In this example, the line has the equation y = (-1/4)x + 15/2. Therefore the data indicates that (conclusion goes here).

Remember, not all data is linear. Sometimes data you get from labs will be in a curved line, like an exponential function. When you get curved data, you can either try to fit a curved line to it (difficult), or modify the axes so that the data appears linear (easy).

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