of Fit and Scatter Plots
Grade Level: 9-10
Time Allotted for Lesson: 90 mins
Number of Students: about 30
I. Goals: The students will
explore scatter plots and lines of best fit. The will learn the
terms positive and negative correlation. They will also learn the
definition of a line of fit and of the best-fit line. We will be
plotting several points of data and determine a best-fit line. We
will write the equation of the best fit line.
II. Objectives: The students
will be exploring best-fit lines. We will plot points and use
Fathom to create data sets and then graph the linear regression lines(
best fit lines). The students will also learn to graph these
lines by hand and determine the equations for the best fit lines.
They will also explore how accurate best fit lines are using a java
III. Materials and Resources: internet
access, Fathom, and computers, graph paper or marker boards with grid
IV. Attention Grabber: Fathom
and internet explorations
Today we will be talking about lines
of fit on scatter plots. There are several terms that we will
need to define first. When we talk about scatter plots we are
talking about several points of data that have been plotted on a graph,
and the line of best fit is the line that most closely goes through the
points of data. We can use the line of best fit to then estimate
new data points, for example if we wanted to know larger values etc.
Scatter Plots: two sets of data are plotted as ordered pairs
Positive correlation: the data is said to have a positive
correlation if the x values increase as the y values increase...for
graphs with positive correlation the lines of best fit also have
Negative correlation: the data is said to have a negative
correlation if the x values increase as the y values decrease, the
slope of the line of best fit will be negative.
Some scatter plots have no correlation. This means that you can
not draw a line of best fit.
Line of fit: if the data points closely resemble a line the a
line of best fit can be drawn.
Line of Best Fit: the line that has the least error margin,
meaning the best-fit line most closely resembles the data.
Let's explore Lines of Best Fit. Go to the following
This simulation allows students to
place data points and find the line of best fit for the points that
they have made. The instructions are on the web. Ask the
students to create one graph that has a positive correlation, one with
a negative correlation. The students should observe that the
positive correlation graph has a best-fit line with positive slope and
the negative correlation with negative slope.
Now we want to explore actual data points, with your graph paper.
Plot the following. (Taken from Glencoe Mathematics Text)
The Table shows an estimate for the number of bald eagle pairs in the
US for certain years since 1985.
Plot these points and draw a line of fit to the data. In your
graph, pick two data points that the line of fit goes through. We
then are going to use those two points to determine the slope and then
write the equation of the line of fit. So, for example if your
points are (3,2500) and (11,5000), then the slope would be
m=2500/8=312.5, and then we would used point slope form so,
y-2500=312.5(x-3), then put the equation into slope intercept
form. y=321.5x + 1562.5.
This is not a line of best fit though, in order to do this we are going
to use fathom and then we are going to see how close our line of fit is
to the actual best-fit line that fathom creates. The computer
program will be the most accurate approximation for the line of best
Refer to your hand out on how to do
From Fathom we get the following.
We can see that our line of fit is fairly close to the line of best fit
from Fathom. Now we want to approximate what may happen in a few
years. So, if we want to know what the number of eagle pairs
there would be 20 years after 1985,
What would be our first step? Do you remember that we said
by writing equations of lines we can determine any value of x or y that
lies on that line if we are given either a x or a y. So if we
have our x=20, how would we find the y that lies on this line?
Plug in our x into the equation of the line of fit we determined and
the line of best fit, let's see how far off our line is.
Line of Fit we calculated:
y= 312.5(20)+1562.5=7812.5 we would round up because cant have half a
pair so there would be 7,813 pairs of eagles 20 years after 1985.
y=309(20)+1560=7740, so there would be approximately 7,740 pairs of
eagles 20 years after 1985 according to the line of best fit from
VI. Closure: Today we
talked about lines of best fit and scatter plots. What were some
advantages to using best fit lines? Can you think of people that
may use best fit lines everyday? (Statisticians) Talk about
other real world examples of scatter plots and lines of best fit.
VII. Extension: This lesson
may take two days, if so take notes and do best-fit lines by hand first
day and computer explorations the second day.