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Correlation and Regression

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As X increases, Y increases, or X and Y change in the same direction. High values of X tend to be paired with high ... Point-biserial correlation coefficient ... – PowerPoint PPT presentation

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Title: Correlation and Regression


1
Correlation and Regression
2
Correlation and Regression
3
Correlation and Regression
  • Purpose Measure Strength of (linear)
    relationship between two variables (X and Y)

4
Uses of Correlation
  • Prediction
  • Typical X ----gt Y
  • Independent/dependent variable
  • Establishing validity
  • Establishing reliability
  • Testing theoretical predictions

5
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

6
Positive Correlation
7
Data Rearranged
8
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

9
Negative Correlation
10
Rearranged Data
Direction versus strength
11
Scatter Plots (Diagrams)
12
Scatter Plots (Diagrams)
Perfect Positive Correlation
13
Scatter Plots (Diagrams)
14
Scatter Plots (Diagrams)
15
Scatter Plots (Diagrams)
16
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

17
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

18
Measuring the Strength of a Correlation
  • R 1 ½ . . .

19
Interpretation of r
  • Restriction of range
  • Coefficient of determination r2
  • Correlation and significance
  • Testing correlation coefficients for significance

20
Related Measures
  • Spearman rank-order correlation coefficient
    (ordinal data)
  • Point-biserial correlation coefficient
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