What is the best fitted line?

serc.carleton.edu - Constructing a best fit line - SERC - Carleton

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How do I construct a straight line through data points?

Best-fit lines

can also be called: Linear regression

Trend lines

Why (and when) should I use a best fit line?

Questions that ask you to draw a best fit line or trend in the data usually do not want you to "connect the dots". Instead, the question is asking you to think about how the two sets of data behave in relation to one another. In general, we fit lines to data when we want to use them for predictive purposes or to determine the general trend of the data.Most scientists use a computer program to plot a best-fit line for a set of data but constructing one for yourself is a good way to learn how it's done. Because a computer isn't doing it, you may find that your "best-fit" line is slightly different from your lab partners. In most cases, that is okay, as long as you've mimicked the trend of the data. In introductory geoscience, most exercises that ask you to construct a best-fit line have to do with wanting to be able recognize relationships among variables on Earth or to predict the behavior of a system (in this case the Earth system). We want to know if there is a relationship between the amount of nitrogen in the water and the intensity of an algal bloom, or we wish to know the relationship of one chemical component of a rock to another. For predictive purposes, we might prefer to know how often an earthquake is likely to occur on a particular fault or the possibility of a very large flood on a given river. All of these applications use best-fit lines on scatter plots (x-y graphs with just data points, no lines). If you find yourself faced with a question that asks you to draw a trend line, linear regression or best-fit line, you are most certainly being asked to draw a line through data points on a scatter plot. You may also be asked to approximate the trend, or sketch in a line that mimics the data. This page is designed to help you complete any of these types of questions. Work through it and the sample problems if you are unsure of how to complete questions about trends and best-fit lines.

How do I construct a best-fit line?

You can also download and print a single sheet for constructing a best fit line with (Acrobat (PDF) PRIVATE FILE 33kB Sep10 08) or (Acrobat (PDF) PRIVATE FILE 34kB Sep10 08) . You can also download and print a single sheet for constructing a best fit line with the area method or the dividing method

Where is this used in the geosciences?

flood frequency curves

earthquake forecasting

Meteorite impact prediction

earthquake frequency vs. magnitude

climate change

A best-fit line is meant to mimic the trend of the data. In many cases, the line may not pass through very many of the plotted points. Instead, the idea is to get a line that has equal numbers of points on either side. Most people start by eye-balling the data.There are many instances in the geosciences where scientists use a best fit line. In the introductory geosciences, we use them for: If you would like to know more about best-fit lines, you can use the links below to read more about them

References and resources

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