7 - Correlation

# 7 - Correlation - Chapter 8 Correlation Oftentimes wish to...

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Chapter 8: Correlation Oftentimes, wish to use values on one variable to predict values on another variable College entrance exams and later grades Income level and health Age and traffic safety

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Want to know the correlation (measure of the degree of relationship between two variables) Greater the correlation, more accurately we can predict value on one variable from value on the other To calculate a correlation, need pairs of observations (scores on each of the two variables; X and Y)
Can get some indication from a bivariate distribution (e.g., frequencies of values in combinations of levels of two variables) 10 30 50 70 90 90 8 18 19 70 5 19 34 16 50 12 21 24 7 30 1 10 14 9 1 10 2 1 Psychology Exam Scores Math Exam Scores

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Scatter Diagram (scatterplot) graphs the bivariate distribution by placing dots at the values of the paired scores
Scatterplot of Economics and Sociology Grades 30 40 50 60 70 80 90 100 30 40 50 60 70 80 90 100 Economics Test Scores

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Correlation coefficients (including Pearson’s r) assume linear relationships between variables Relation that can be represented by a straight line
Scatterplot of Economics and Sociology Grades 30 40 50 60 70 80 90 100 30 40 50 60 70 80 90 100 Economics Test Scores

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Direction of a Correlation Positive Correlation As values on X increase, values on Y tend to
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7 - Correlation - Chapter 8 Correlation Oftentimes wish to...

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