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1.5 Scatter Plots and Lines of Best FitEssential Questions: How can I use ascatter plot to draw informal inferenceabout the correlation between twovariables? How do I determine an equationfor the line of best fit using a graphingcalculator?
In many realworld problems, youwill find data that relate twovariables such as time anddistance or age and height. Youcan view the relationship betweentwo variables with a scatter plot.
A scatter plot is the graph of the ordered pairs that describe
a relationship betweentwo sets of data.
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Correlation
Positive correlation Negative correlation
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6 5 4 3 2 1 0 1 2 3 4 5 6
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Correlation continued
No correlation
6 5 4 3 2 1 0 1 2 3 4 5 6
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Let's collectsome data.
Name Age (in years)
Height(in inches)
Wingspan(in inches)
# of Letters in Last Name
Hattie
Corey
Jason
Tay
Alexis
Evan
Lewis
Egypt
Dazasha
Tyler
Mike
Carly
Briyona
Dre
Casey P.
Mat
Tory
Casey S.
Kali
Krystin
Alexa
Morgan
Melanie
Lexi
Erika
Haimbach
Monique
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Line of Best Fit
A scatter plot can help you see patterns in data involving two variables. A line of best fit is a linear model that fits that data.
Part 1: Input the data from the table into your calculator:1) Stat2) Edit3) Input ages into L1, height into L2, wingspan into L3, and number of letters in last name in L4
Part 2: Make it so that you will be able to see the points on a graph:
1) 2nd2) Y =3) Go into the first stat plot4) Turn the stat plot on5) Make sure that L1 is used for x and L2 is used for y
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Line of Best Fit continued
Part 3: View the graph:1) Window2) Find the minimum and maximum values for x from the table. Set appropriate values for the xmin, xmax, and xscl.3) Find the minimum and maximum values for y from the table, and set appropriate values for the ymin, ymax, and yscl.4) Graph
Part 4: Write the line of best fit:1) Stat2) Calc3) 4: LinReg (ax + b) L1, L24) EnterThis gives you the equation for the line of best fit.
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Correlation Coefficient
The correlation coefficient is a number represented by the variable, r, that describes how closely points in a scatter plot cluster around the line of best fit.
When the rvalue is close to 1 or 1, the line of best fit is a good representation of the data.
Positive rvalue = positive correlationNegative rvalue = negative correlationZero (or close to zero) rvalue = no correlation
What is the correlation coefficient of the line of best fit for the data you graphed?
Is there a correlation between the height and wingspan of students in this class?
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Practice
With the person sitting next to you, choose two columns of the table.
1) Plot the points on a graph in your calculator. Sketch the graph.2) Write the line of best fit.3) Find the correlation coefficient.4) Is there a correlation between the two sets of data you chose?
How do you know that there is or isn't a correlation?