Math You Need > Graphing > Constructing a best fit line > Best fit line - Sample problems

# Adding a trend line to a scatter plotConstructing a best-fit line - Sample Problems

Below you will find practice problems for constructing a best fit line using the steps found on the introduction pages. Try to do them without looking at the answers first.

You can download and print a single sheet for constructing a best fit line with the area method (Acrobat (PDF) 33kB Sep10 08) or the dividing method (Acrobat (PDF) 34kB Sep10 08) as well as a sheet with all the questions (Acrobat (PDF) 124kB Jul25 09) so that you can practice them.

## Plate motion problem

Hawaii is a hot spot, a volcano that is generated by a fixed plume of magma. The Pacific plate moves over the hot spot and we can use the location of a volcano through time to determine the rate at which the Pacific plate moves. The graph below shows a plot of the age of volcanoes vs. location relative to Kilauea (the present active volcano). One way to determine average plate motions is to use the trend of the data. Construct a best-fit line for the data on the plot below for the Hawaiian hotspot. You may wish to download and print the plot shown below (Acrobat (PDF) 47kB Sep9 08).
Remember that there are two possible ways to construct a best-fit line by eye. You may use either of them.
1. Begin by plotting all your data. In this case you are given the points already plotted, so you can skip this step. If you don't know how to plot points, please visit the plotting points page

2. Draw a shape that encloses all of the data, (try to make it smooth and relatively even).
3. Draw a line that divides the area that encloses the data in two even sized areas. In other words, bisect the area with a line that goes from one edge of the plot to the other.
4. You have just constructed a best fit line through the data!
Note that it is not necessary for the line to pass through ANY of the points on the plot, it is only important that your line bisect (cut in half) the area that encloses the data points. Now you can use the line to predict behavior. Or, you can examine the other method and try it out.
1. Begin by plotting all of your data. In this case you are given the points already plotted, so you can skip this step. If you don't know how to plot points, please visit the plotting points page

2. Draw a line that divides the data in two (even numbers of points on either side of the line)

In this case, there are 39 points on the graph, so, to the best of your ability, draw a line that has approximately 19.5 points on either side of it.
3. Place an x (or a + or a dot) in your interpretation of the center of the data on either side of the line.

Your x marks may not be in exactly the same place as mine - that's okay, we all see things slightly different. They shouldn't be too far off though.
4. Connect the x marks with a line that extends to the edges of the plot.
5. Congratulations! You have just constructed a best fit line through the data!
Note that it is not necessary for the line to pass through ANY of the points on the plot, it is only important that your x marks are in the center of the plotted data and your line connects those x marks.

## Glacial Retreat problem

Global climate change has affected mountain glaciers all over the world. At Nisqually Glacier on Mount Rainier in Washington State, scientists have measured the retreat of the glacier from 1858 through 1994. The data from 1858-1994 is plotted on the graph below, using the location in 1994 as the 0 km point. Construct a best fit line through the data. You may wish to download and print the plot shown below (Acrobat (PDF) 23kB Sep9 08).
Remember that there are two possible ways to construct a best-fit line by eye. You may use either of them.
1. Begin by plotting all your data. In this case you are given the points already plotted, so you can skip this step. If you don't know how to plot points, please visit the plotting points page

2. Draw a shape that encloses all of the data, (try to make it smooth and relatively even).
3. Draw a line that divides the area that encloses the data in two even sized areas. In other words, bisect the area with a line that goes from one edge of the plot to the other.
4. You have just constructed a best fit line through the data!
Note that it is not necessary for the line to pass through ANY of the points on the plot, it is only important that your line bisect (cut in half) the area that encloses the data points. Now you can use the line to predict behavior. Or, you can examine the other method and try it out.
1. Begin by plotting all of your data. In this case you are given the points already plotted, so you can skip this step. If you don't know how to plot points, please visit the plotting points page

2. Draw a line that divides the data in two (even numbers of points on either side of the line)

In this case, there are 17 points on the graph, so, to the best of your ability, draw a line that has approximately 8.5 points on either side of it.
3. Place an x (or a + or a dot) in your interpretation of the center of the data on either side of the line.

Your x marks may not be in exactly the same place as mine - that's okay, we all see things slightly different. They shouldn't be too far off though.
4. Connect the x marks with a line that extends to the edges of the plot.
5. Congratulations! You have just constructed a best fit line through the data!
Note that it is not necessary for the line to pass through ANY of the points on the plot, it is only important that your x marks are in the center of the plotted data and your line connects those x marks.

## Flooding problem

Many communities built on flood plains want to know whether a flood will impact their lives. Geoscientists can give inhabitants an estimate of the probability of a flood hitting an area based on past patterns. Below is a plot (on a type of graph paper called semi-log, where the x-axis is a logarithmic scale) of the probability of a river rising to a given stage (meters above normal). Construct a best fit line through the data. You may wish to download and print the plot shown below (Acrobat (PDF) 22kB Sep9 08).
Remember that there are two possible ways to construct a best-fit line by eye. You may use either of them.
1. Begin by plotting all your data. In this case you are given the points already plotted, so you can skip this step.

2. Draw a shape that encloses all of the data, (try to make it smooth and relatively even).
3. Draw a line that divides the area that encloses the data in two even sized areas. In other words, bisect the area with a line that goes from one edge of the plot to the other.
4. You have just constructed a best fit line through the data!
Note that it is not necessary for the line to pass through ANY of the points on the plot, it is only important that your line bisect (cut in half) the area that encloses the data points. Now you can use the line to predict behavior. Or, you can examine the other method and try it out.
1. Begin by plotting all of your data. In this case you are given the points already plotted, so you can skip this step.

2. Draw a line that divides the data in two (even numbers of points on either side of the line)

In this case, there are 17 points on the graph, so, to the best of your ability, draw a line that has approximately 8.5 points on either side of it.
3. Place an x (or a + or a dot) in your interpretation of the center of the data on either side of the line.

Your x marks may not be in exactly the same place as mine - that's okay, we all see things slightly different. They shouldn't be too far off though.
4. Connect the x marks with a line that extends to the edges of the plot.
5. Congratulations! You have just constructed a best fit line through the data!
Note that it is not necessary for the line to pass through ANY of the points on the plot, it is only important that your x marks are in the center of the plotted data and your line connects those x marks.

## Next Steps

Think you understand? Then go to wamap.org to take the online quiz.

If you still need help, you can go back to the explanation page or look at some of the links below.

## Need more practice?

The Argyll center in Canada has some problems where you can practice making scatter plots and fitting lines to the data.