|
line of
best fit, range, interpolate, extrapolate, lower extreme, upper extreme, trend, independent variable,
dependent variable,
discreet variable, continuous variable, positive correlation,
negative
correlation, weak
correlation, strong
correlation
Interactive Component Under Construction
|
Learning Outcomes:
The student will:
| line of best fit (trend line) - A line on a scatter plot
which can be drawn near the points to more clearly show the trend between two sets of
data. The data is used to derive a curve of best fit. 
|
Line of Best Fit
The correlation coefficent (r) ranges between -1 and 1. It is part of the
following applet, but will not critical to this lesson. It is useful, however to help us
understand the strength of data correlations.
| Correlation |
Strong |
Weak |
| Positive |
0.7 to 1.0 |
0.3 to 0.7 |
| Negative |
-1.0 to -0.7 |
-0.7 to -0.3 |
Little or No Correlation: -0.3 to
0.3 |
Line of Best Fit
Add up to 50 points onto the green viewing screen by clicking on the screen with the
mouse, a red line represents a line passing through (Average
x, Average y). The slope of the red line can be altered
by clicking the Left or Right buttons on the "Rotation Scroll Bar". By
clicking on Show Best Fit, a blue best fit line
will also appear.
The slope of red line may be changed by dragging the mouse
either right or left.
The thermometer on the right measures how well the red
line fits the data points. If the thermometer measures a good fit (that is, small
error) then the red line is a good fit to the data..
Applet
Source, Written by Nicholas Exner
download source: Java Applets and Activities
|
| Directions: Use the following to plot points on a
scatter plot. Click on the grid several times and observe what happens to the line
of best fit for a linear relationship. Click the "Clear Points" button. Click
on two points on the grid. The points will be connected by a line. See what
happens if you click on other points on the line.
Click the "Clear Points" button. Click on two points on the grid. The
points will be connected by a line. See what happens if you click on grid points
that are not on the line.
- Click and drag data points to change their positons.
- The value of r is the correlation coefficent. It ranges between -1 and 1.
It is part of the applet, but will not be emphasized in this lesson. It
is useful, however to help us understand the strength of data correlations.
source: http://ictcm.tamu.edu/Scatterplot/index.html
|
Directions: Use the
following to examine 3 scatterplot samples and to create your
own scatterplots.
- Click the "Load Data File" button to see the
first scatterplot sample. The other two samples
are available from the pulldown menu. To display
the sample, click the "Load Data File" button
after selecting a sample. Click on various spreadsheet
cells and change the values. Notice the effect the
change has on the line of best fit.
- Create your own scatterplots by entering the data points
into the spreadsheet to the left of the graph.
- The correlation coefficent ranges between -1
and 1. It is part of the applet, but will not
be emphasized in this lesson. It is useful,
however to help us understand the strength of data
correlations.
source:
http://ictcm.tamu.edu/Wisconsin_2001/Scatterplot/
source: http://math.hws.edu/javamath/config_applets/index.html |
| Directions: Use the following to plot points on a
scatter plot. Click on the grid several times and observe what happens to the line
of best fit for a linear relationship. Click the "Clear Points" button. Click
on two points on the grid. The points will be connected by a line. See what
happens if you click on other points on the line.
Click the "Clear Points" button. Click on two points on the grid. The
points will be connected by a line. See what happens if you click on grid points
that are not on the line.
- Click and drag data points to change their positons.
- The value of r is the correlation coefficent. It ranges between -1 and 1.
It is part of the applet, but will not be emphasized in this lesson. It
is useful, however to help us understand the strength of data correlations.
To interpolate, click a point on the line between
the outer most points on the curve.
To extrapolate, click a point on line of best fit
outside of the other points on the curve.
source: http://ictcm.tamu.edu/Wisconsin_2001/Scatterplot/
|
Directions: Use the following to examine 3
scatterplot samples and to create your own scatterplots.
- Click the "Load Data File" button to see the first scatterplot sample.
The other two samples are available from the pulldown menu. To display the sample,
click the "Load Data File" button after selecting a sample. Click on various
spreadsheet cells and change the values. Notice the effect the change has on the
line of best fit.
- Create your own scatterplots by entering the data points into the spreadsheet to the
left of the graph.
- The correlation coefficent ranges between -1 and 1. It is part of the applet,
but will not be emphasized in this lesson.
- The slope and intercept of the line of best fit is given, but will not be emphasized
in this lesson.
To interpolate, plot the point on the line between
the outer most points on the curve.
To extrapolate, plot the point on curve of best
fit outside of the other points on the curve.
source: http://math.hws.edu/javamath/config_applets/index.html |
|
