# UNM STAT 145 - Chapter 3 CORRELATION AND REGRESSION (32 pages)

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## Chapter 3 CORRELATION AND REGRESSION

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## Chapter 3 CORRELATION AND REGRESSION

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Lecture Notes

Pages:
32
School:
University of New Mexico
Course:
Stat 145 - Introduction to Statistics
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Chapter 3 CORRELATION AND REGRESSION TOPIC SLIDE Correlation Defined 3 Range of the Correlation Coefficient 6 Scatter Plots 9 Null and Alternative Hypotheses 12 Statistical Significance 16 Example 1 21 Example 2 24 Coefficient of Determination 28 Tutorials Obtaining the Correlation Coefficient in Excel 2007 Chapter 3 CORRELATION Chapter 3 CORRELATION Indicates how well the ranking of scores on one variable matches the ranking of scores on a second variable As the ranking of scores on the first variable increasingly match the ranking of scores on the second variable the correlation will be stronger The fewer matched rankings the weaker the correlation Chapter 3 CORRELATION The ranking of scores may match in the same direction i e the score ranked first on variable 1 is also ranked first on variable 2 or opposite direction i e the score ranked first on variable 1 is ranked last on variable 2 There is no correlation when the ranking of scores on one variable fail to match any of the scores on the second variable Chapter 3 CORRELATION EXAMPLE Five soccer players were ranked according to their soccer ability and their grade point average GPA Perfect Positive r Perfect Negative r Soccer Player Ability A 1 B 2 C 3 D 4 E 5 Soccer Player Ability GPA A 1 5 B 2 4 C 3 3 D 4 2 E 5 1 GPA 1 2 3 4 5 Chapter 3 CORRELATION The numeric value of the correlation coefficient has a range of 1 00 to 1 00 where zero indicates no correlation The closer the correlation coefficient is to 1 00 or 1 00 the stronger the correlation between two variables The closer the correlation coefficient is to 0 the weaker the correlation between two variables A correlation coefficient equal to 0 means there is no correlation between two variables Which value represents a stronger correlation 65 or 85 Chapter 3 CORRELATION The correlation coefficient describes two characteristics The sign of the correlation positive or negative indicates the direction of the relationship between the two variables The value of

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