6.pdf - Correlation ❖ Y = f(X ❖ where Y is Dependent...

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Correlation Y = f(X), where Y is Dependent variable or the result (output) X is Independent variable, input or the controllable variable For example in the study of marks obtained by students in a subject (Y) vs hours of study (X)
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Correlation
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Correlation
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Correlation Demonstration: Calculate Pearson’s Correlation coefficient using MS Excel Column 1 Column 2 Column 1 1 Column 2 0.879350768 1
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Correlation Coefficient Correlation Measures the strength of linear relationship between Y and X Pearson Correlation Coefficient, r (r varies between -1 and +1) Perfect positive relationship: r = 1 No relationship: r = 0 Perfect negative relationship: r = -1
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Correlation Coefficient
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Correlation vs Causation Correlation does not imply causation a correlation between two variables does not imply that one causes the other
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Correlation Confidence Interval Population correlation ( ρ) – usually unknown Sample correlation (r)
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Correlation Confidence Interval Since r is not normally distributed, there are three steps to find out confidence interval Convert r to z’ (Fisher’s Transformation) Calculate confidence interval in terms of z’ Convert confidence interval back to r z’ = .5[ln(1+r) – ln(1-r)] Variance = 1/N-3
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