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H OW TECHNOLOGY CAN MAKE MY LIFE EASIER WHEN GRAPHING ! Compute (using technology) and interpret the correlation coefficient of a linear fit. MAFS.912.S-ID.3.8

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T HE C ORRELATION C OEFFICIENT Real World Data What do you see? In your groups discuss the graph.

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L ESSON WARM - UP Lets review the correlation of scatter plots Do the following graphs have, POSITIVE, NEGATIVE or NO CORRELATION?

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L ESSON WARM - UP POSITIVE, NEGATIVE or NO CORRELATION? NEGATIVE POSITIVE NO CORRELATION CORRELATION CORRELATION

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L ESSON WARM - UP POSITIVE, NEGATIVE or NO CORRELATION? NEGATIVE POSITIVE NO CORRELATION CORRELATION CORRELATION * Decreases or * Increases or * No pattern goes down goes up points all from left to right from left to right over the graph

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L ESSON WARM - UP LINE OF BEST FIT Could you draw a line through the middle of the data?

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L ESSON WARM - UP LINE OF BEST FIT Could you draw a line through the middle of the data? Drawing the line of best fit Draw a line right through the middle of the data, with roughly the same number of points above the line as below the line.

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T HE C ORRELATION C OEFFICIENT What is the correlation coefficient?

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T HE C ORRELATION C OEFFICIENT What is the correlation coefficient? http://tube.geogebra.org/student/m128082 What can you do with this tool? What do you notice?

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T HE C ORRELATION C OEFFICIENT What is the correlation coefficient? The correlation coefficient is a number between -1 and 1 that shows the strength and type of relationship between two variables. The correlation coefficient can be referred to as “R”

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T HE C ORRELATION C OEFFICIENT What would that look like on a graph? If the correlation coefficient “R” number is: Between -1 and 0 0 Between 0 and 1

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T HE C ORRELATION C OEFFICIENT What would that look like on a graph? If the correlation coefficient “R” number is: Between -1 and 0 0 Between 0 and 1

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T HE C ORRELATION C OEFFICIENT What is the correlation coefficient? If the correlation coefficient “R” number is: Between -1 and 0 0 Between 0 and 1 The correlation The correlation is negative No correlation is positive

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T HE C ORRELATION C OEFFICIENT What would that look like on a graph? If the correlation coefficient “R” number is: Between -1 and 0 0 Between 0 and 1 Negative No Positive Correlation Correlation Correlation

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T HE C ORRELATION C OEFFICIENT Is the correlation coefficient weak or strong? For the negative correlation, if the correlation coefficient “R” number is: Closer to -1 Closer to 0 The correlation The correlation is strong is weak

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T HE C ORRELATION C OEFFICIENT Is the correlation coefficient weak or strong? For the NEGATIVE correlation, if the correlation coefficient “R” number is: Closer to -1 -0.5 Closer to 0

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T HE C ORRELATION C OEFFICIENT Is the correlation coefficient weak or strong? For the negative correlation, if the correlation coefficient “R” number is: Closer to -1 -0.5 Closer to 0 NEGATIVE STRONG NEGATIVE WEAK

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T HE C ORRELATION C OEFFICIENT Is the correlation coefficient weak or strong? For the positive correlation, if the correlation coefficient “R” number is: Closer to 0 Closer to 1 The correlation The correlation is weak strong

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T HE C ORRELATION C OEFFICIENT Is the correlation coefficient weak or strong? For the POSITIVE correlation, if the correlation coefficient “R” number is: Closer to 0 0.5 Closer to 1

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T HE C ORRELATION C OEFFICIENT Is the correlation coefficient weak or strong? For the POSITIVE correlation, if the correlation coefficient “R” number is: Closer to 0 0.5 Closer to 1 POSITIVE WEAK POSITIVE STRONG

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M ATCHING G AME In your groups: Take the matching game worksheet and cut out and separate the: * 4 graphs * 4 Descriptions * 4 “R” numbers * Correlation Types * Correlation Strength Now in your groups work together to match the: Graph Description “R” number Correlation Strength Correlation Type

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G ROUP T ASK : In your groups: You will work together to complete your task. You will be graphing two measurements of your choice, such as: Height Foot length Arm length You will work together to: Create a graph on paper to predict the correlation Create a graph electronically using GeoGebra software to confirm the correlation coefficient.

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C ALCULATING THE CORRELATION COEFFICIENT It can be calculated using technology such as excel or GeoGebra – we will be using GeoGGebra today. http://www.trialrun.com/pop-ups/pearsons_correlation.html

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G ROUP T ASK II: Using GeoGebra You will work together to complete your task. The worksheet will ask you questions, you must answers these in full sentences! Enter the data into GeoGebra Create a graph Add a Line of Best Fit Find the statistics of the data Locate the Correlation Coefficient “R”

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