## Scatter Plot and Line of Best Fit

scatter plot - a graph that relates data from two different sets.

Directions:  Use the following interactive grid to create your own scatter plot(s).

1. Click on the grid several times to plot data points. Look for a pattern. Can you see a trend emerging in the scatter plot data?
2. Click "Reset" to clear the data if you wish to make additional scatter plots.
 independent variable

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.

1. 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.
2. 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.
3. 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.
4. 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.

1. 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.
2. 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.

1. 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.
2. If you would like additional information for one of the graph features, select the "Rollover help" checkbox, then move your mouse over the feature.