 # Copyright © 2011 Pearson Education, Inc. Slide 5-1 Unit 5E Correlation Coefficient.

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Copyright © 2011 Pearson Education, Inc. Slide 5-1 Unit 5E Correlation Coefficient

Copyright © 2011 Pearson Education, Inc. Slide 5-2 Unit 5E What does it tell us?

5-E Copyright © 2011 Pearson Education, Inc. Slide 5-3 The trendline is simply a straight line fitted to the data by the method of least squares. If the straight line goes “uphill,” it indicates a positive correlation. If the straight line goes “downhill,” it indicates a negative correlation. If the straight line is horizontal or nearly horizontal, it indicates no correlation Review: Trendline

5-E Copyright © 2011 Pearson Education, Inc. Slide 5-4 The correlation coefficient is a measure of the strength of the correlation (i.e., how near the data are to the trendline) If the straight line goes “uphill,” R will have a positive value; the closer R is to 1, the stronger the correlation If the straight line goes “downhill,” R will have a negative value; the closer R is to -1, the stronger the correlation If the straight line is horizontal or nearly horizontal, R will be zero or have a very small value Review: Correlation Coefficient R r

5-E Four Sets of Data over the same Range Copyright © 2011 Pearson Education, Inc. Slide 5-5 xyy1y2y3 0.002.002.101.000.00 1.003.002.904.005.00 2.004.003.103.002.00 3.005.004.906.007.00 4.006.005.905.004.00 5.007.007.108.009.00 6.008.007.907.006.00 7.009.009.1010.0011.00 8.0010.009.909.008.00 9.0011.0011.1012.0013.00

5-E Scatterplot of Y Data Set (Correlation?) Copyright © 2011 Pearson Education, Inc. Slide 5-6

5-E Scatterplot for Y1 Data Set (Correlation?) Copyright © 2011 Pearson Education, Inc. Slide 5-7 R=0.995935

5-E Scatterplot for Y2 Data Set (Correlation?) Copyright © 2011 Pearson Education, Inc. Slide 5-8

5-E Scatterplot of Y3 Data Set (Correlation?) Copyright © 2011 Pearson Education, Inc. Slide 5-9

5-E Copyright © 2011 Pearson Education, Inc. Slide 5-10 Match a Correlation Coefficient to a Scatter Plot Given R = 0.801569 Which of the following scatter plots could have this correlation coefficient?

5-E Copyright © 2011 Pearson Education, Inc. Slide 5-11 Match this Correlation Coefficient to Scatter Plot Number 1? R = 0.801569

5-E Copyright © 2011 Pearson Education, Inc. Slide 5-12 Match This Correlation Coefficient to Scatter Plot Number 2? R = 0.801569

5-E Copyright © 2011 Pearson Education, Inc. Slide 5-13 Match This Correlation Coefficient to Scatter Plot Number 2? No! R = 0.801569

5-E Copyright © 2011 Pearson Education, Inc. Slide 5-14 Match this Correlation Coefficient to Scatter Plot Number 3? R = 0.801569

5-E Copyright © 2011 Pearson Education, Inc. Slide 5-15 Match this Correlation Coefficient to Scatter Plot Number 3? No! R = 0.801569

5-E Copyright © 2011 Pearson Education, Inc. Slide 5-16 Match this Correlation Coefficient to Scatter Plot Number 1? R = 0.801569

5-E Copyright © 2011 Pearson Education, Inc. Slide 5-17 Match this Correlation Coefficient to Scatter Plot Number 1? Yes! R = 0.801569 R 2  64% Data within Trendline Relationship  Matches