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 line of best that rises quickly from left to right is called a
positive correlation.
The line of best that falls down quickly from left to the right is
called a negative correlation
Strong positve and negative correlations have data
points very close to the line of best fit..
Weak positve and negative correlations have data
points that are not clustered near or on the line of best fit.
Data points that are not close to the line of best fit are called
outliers.
Directions: Use the following interactive
grid to create a scatter plot. Study the changes in the line
of best fit as you add additional data points.
Create a scatter plot with a line of best fit showing a positive
correlation. Click "Reset" to
clear the data if you wish to make additional scatter plots.
Create a scatter plot with a line of best fit showing a negative correlation.
Click "Reset" to clear the data
if you wish to make additional scatter plots.
Create a scatter plot with a line of best fit showing little or no
correlation. Click "Reset" to
clear the data if you wish to make additional scatter plots.
Notice a scatter plot with a strong correlation has
data points clustered very near to the line of best fit. Weak
correlations have data points that are further from the line
of best fit. Create a scatter plot with a line of best fit showing weak
positive and weak negative correlation. Click "Reset"
to clear the data if you wish to make additional scatter plots.
Interpolate is the process one uses to
determine a value on the line of best fit within the cluster of scatter
plot data.
Extrapolate is the process one uses to
determine a value on the line of best fit outside the range of data values
plotted. Extrapolated values on a line of best fit are outside the cluster
of scatter plot data.
Directions: Use the following interactive grid
to create a scatter plot. Study the changes in the line
of best fit as you add additional data points.
Click on the grid several times to plot data points. Practice interpolating
data. Pick a value on the x-axis that is inside the cluster
of points. Follow the point upwards until your reach the line of best
fit. Estimate the y-axis value for this point on the line of best fit.
Click on the point to check your estimate. If the line of best fit does
not move - congratulations! Click "Reset"
to clear the data.
Practice extrapolating data. Pick a value on the
x-axis that is outside the cluster of points that determine the line
of best fit. Follow the point upwards until your reach the line of best
fit. Estimate the y-axis value for this point on the line of best fit.
Click on the point to check your estimate. If the line of best fit does
not move - your estimate is great! Click "Reset"
to clear the data.
Enrichment: The correlation
coefficent (r) ranges between -1 and 1. For this course
you do not have toremember these value. The scale on the right
of the grid includes the correlation coefficient. Notice the black
regions are positive correlatioins and the red are negative correlations.
My students will need to be able to classify
scatter plot patterns as strong/weak positive, strong/weak negative
or no correlation. This next activity will help you see
the mathematical pattern of correlation that you may study in
high school.
Directions: Use this interactive
graph to study line of best fit and correlation of scatter plots.
Click "New Sample" to generate
another set of data.
Click and drag the red slider on the right to change the correlation.
Study the scatter plot and line of best fit as you move the
slider.
If you would like additional information for one of the graph
features, select the "Rollover help"
checkbox, then move your mouse over the feature.