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Correlation

Correlation measures the strength and direction of the linear relationship between two continuous variables, such as height and weight. It ranges from -1 to 1, indicating the degree of linear association: 1 for perfect positive correlation, -1 for perfect negative correlation, and 0 for no correlation. Key assumptions include normality and linearity. The correlation coefficient (r) is derived from covariance, indicating how closely scores on variables move together. Understanding these concepts helps in analyzing data relationships effectively.

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Correlation

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  1. Correlation

  2. Overview Defined: The measure of the strength and direction of the linear relationship between two variables. Variables: IV is continuous, DV is continuous Relationship: Relationship amongst variables Example: Relationship between height and weight. Assumptions: Normality. Linearity.

  3. Strength: ranges from 0 to 1 (or -1)Direction: positive or negative See this link for interactive way to look at scatterplots

  4. Correlation Coefficient • A measure of degree of relationship. • Based on covariance • Measure of degree to which large scores go with large scores, and small scores with small scores • Covariance Formula = Covxy = Σ(X-X)(Y-Y) • Correlation Formula = r = Covxy (SSx)(SSy)

  5. r = Σ(X-X)(Y-Y) = CovXY Σ[(X-X)2][(Y-Y)2] (SSX)(SSY) • r = 900 = 900 = .90 (100,000)(10) 1000

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