Correlation and Regression

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Correlation and Regression
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Correlation and Regression
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Correlation and Regression

• Purpose Measure Strength of (linear)
  relationship between two variables (X and Y)

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Uses of Correlation

• Prediction
• Typical X ----gt Y
• Independent/dependent variable
• Establishing validity
• Establishing reliability
• Testing theoretical predictions

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Describing Relationships

• Positive Correlation
• As X increases, Y increases, or X and Y change in
  the same direction
• High values of X tend to be paired with high
  values of Y, etc.
• Rearrangement of Y values when X put in order

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Positive Correlation
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Data Rearranged
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Negative Correlation

• As X increases, Y decreases/X and Y change in
  opposite directions
• High values of X tend to be paired with high
  values of Y, etc.
• Rearrangement of Y values when X put in order

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Negative Correlation
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Rearranged Data
Direction versus strength
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Scatter Plots (Diagrams)
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Scatter Plots (Diagrams)
Perfect Positive Correlation
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Scatter Plots (Diagrams)
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Scatter Plots (Diagrams)
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Scatter Plots (Diagrams)
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Measuring the Strength of a Correlation

• Pearson-Product Moment Correlation Coefficient
  (Pearson r)
• Variance Interpretation of Correlation r ratio
  of shared variance (co-variance) between X and Y
  to the total variance of X and Y separately

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Measuring the Strength of a Correlation

• Z-Score Interpretation of Correlation
  Correlation reflects the size of the difference
  between paired Z-scores
• Mean of squared differences between paired z
  scores
• Perfect positive correlation 0
• No correlation 2
• Perfect negative correlation 4

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Measuring the Strength of a Correlation

• R 1 ½ . . .

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Interpretation of r

• Restriction of range
• Coefficient of determination r2
• Correlation and significance
• Testing correlation coefficients for significance

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Related Measures

• Spearman rank-order correlation coefficient
  (ordinal data)
• Point-biserial correlation coefficient