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Understanding Correlation and Regression: Key Concepts in Statistical Analysis

This section covers essential principles of correlation and regression, emphasizing the importance of plotting data before analysis to identify linear relationships. It highlights the potential for distortion by extreme values and the risks associated with extrapolation beyond the data range. Lurking variables can misrepresent relationships, with correlations often overstated when based on averaged data. Distinctions between correlation and causation are clarified, underlining the necessity of controlled experiments to establish true causal relationships.

alastair-scott
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Understanding Correlation and Regression: Key Concepts in Statistical Analysis

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  1. Interpreting Correlation and Regression Section 4.2

  2. Correlation and Regression • Describe only linear relationship. • Strongly influenced by extremes in data. • Always plot data first. • Extrapolation – Use of regression line or curve outside the values of the domain of explanatory variable.

  3. Averaged Data • Correlations based on averages, not actual data, are usually too high. • Smooths out data. • Does not allow for scatter among individuals.

  4. Lurking Variables • Variables that influence the two studied variables but are not in the study. • Can falsely suggest a strong relationship. • Can hide a relationship. • Ex: Herbal tea in nursing homes/Ice cream and drowning.

  5. Association does not imply Causation • Strong associations ≠ cause/effect relation. • Causation – Change in x causes change in y. • Common Response – Both x and y respond to changes in some unobserved variable. • Confounding – The effect on y of x is mixed up with effects on y of other variables.

  6. Lurking Variables

  7. Experiments • Best way to get good evidence that x causes y. • Only x is changed, while lurking variables are controlled.

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