Transcript Unit 3.1 - LincolnLions.org

Unit 3.1
Scatter Plots & Line of Best Fit
Scatter Plots
• Scatter Plots are graphs of (X,Y) data
• They are constructed to show a mathematical
relationship between the data.
• A line of best fit is often drawn to state the
mathematical relationship as an equation.
• The relationship may be negative (negative slope)
or positive (positive slope)
• Also the relationship may be strong or weak.
Scatter plot animation Correlation Demo
What is correlation?
• Numerical measure used to show the strength and
direction of a linear association between 2 variables
• Abbreviation for correlation is r.
• The value of r is always between -1 and 1. Values of -1
or 1 have a strong linear association, while values near
0 have a weak or no correlation.
• Correlation is NOT RESISTANT, so outliers or extreme
values can greatly affect the value of r.
Graphs Showing Correlation
Do the following graphs have strong/weak and
positive/negative correlations?
Writing “Line of Best Fit”
• Graph the (x,y) pairs on the graph.
• Look for a line (use a ruler) that seems to be in the
middle of the data. Does not have to go through any
of the points but it might.
• Find two points on the line and use them to calculate
the slope.
• Use the slope and one of the points to solve for the y
intercept. Write equation in slope intercept form. Y
= mx + b
Accuracy of Line of Best Fit
These things affect the accuracy of line of best fit:
• The more data points you have (bigger sample size),
the more accurate your line will be.
• The fewer extreme values (outliers) you have, the
better your line will be.
• The higher the correlation (closeness of data points
to each other in a linear pattern), the better your line
will be.
Creating a Scatter plot by Hand
• Chirping crickets - CricketsChirpActivity.pdf
• Excel solution - Temp vs Cricket chirps.xls