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WEBVTT

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In this video, we will discuss how to fit a trendline to your data.

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We will talk about how to choose a trendline, how to use the r-squared value, and what minimum

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and maximum lines are.

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Your trendline is evaluated under the analysis criterion.

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It might be nonlinear or linear.

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Students often think that the trendline must be linear.

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This is not true.

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If your trendline is clearly nonlinear, please do not try to force a linear fit.

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Finally, your trendline should pass through all error bars.

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Let's see how I chose my trendline in the example IA.

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I am using the numbers program on a MacBook Air to fit different trendlines.

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It is clear from my data points that my trendline will not be linear.

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This is confirmed when I try to fit a linear trendline.

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The trendline clearly does not go through all error bars, and the r-squared value, 0.799,

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is relatively low.

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When I tried a logarithmic or exponential fit, I did not get a trendline.

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Next I tried different polynomial fits, in other words x-squared, x-cubed, and x to the

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power of four type of functions.

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This is what I got for x-squared, for x-cubed, and for x to the power of four.

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Based on the r-squared value, all three seem to be good fits.

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In the end, I chose the function with x to the power of four, in other words, a polynomial

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of order four, because visually it seems to pass through all the error bars, and it also

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has the highest r-squared value.

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On the graph in my IA, I will not show the equation and the r-squared value, but I will

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briefly come back to them later.

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So this is how the final graph looks like in the example IA.

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The r-squared value, as we said, basically shows how well a trendline fits your data.

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The closer r-squared is to one, the better the fit.

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Finally, there is no need to calculate r-squared by hand.

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Just use the graphing program to do this.

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If your trendline is linear, you should find the minimum and maximum lines.

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In this case, you should show three lines on your graph.

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The best fit line, the line with the lowest, and the line with the highest gradient.

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Finally, in some cases, when your trendline is not linear, you might have to linearize

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your graph.

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We will discuss this in a separate video.

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This completes step six, action three.

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Now you know how to fit a trendline to your data.

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In the next video, we will discuss how to interpret your data.