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2.4: Cautions about Regression and Correlation

Learn about the cautions when using regression and correlation analysis. Understand the limitations of correlation, dangers of extrapolation, issues with lurking variables, influential data points, and more.

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2.4: Cautions about Regression and Correlation

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  1. 2.4: Cautions about Regression and Correlation

  2. Cautions: Regression & Correlation • Correlation measures only linear association. • Extrapolation often produces unreliable predictions. • Correlation and least-squares regression are not resistant. • Lurking variables can make a correlation or regression misleading.

  3. Residual Plots • A residual plot is a scatterplot of the regression residuals (i.e., errors) against the explanatory variable. • Residual plots make patterns in the original scatterplot of data more apparent. • If the regression catches the overall pattern of the data, there should be no evident pattern to the residuals.

  4. Cautions: Regression & Correlation • Correlation measures only linear association. • Extrapolation often produces unreliable predictions. • Correlation and least-squares regression are not resistant. • Lurking variables can make a correlation or regression misleading.

  5. Cautions: Regression & Correlation • Correlation measures only linear association. • Extrapolation often produces unreliable predictions. • Correlation and least-squares regression are not resistant. • Lurking variables can make a correlation or regression misleading.

  6. Outliers & Influential Data Points • Remember, an outlier is an observation that lies outside the overall pattern of the other observations. • In a least-squares regression, does an outlier have to have a large residual?

  7. Outliers & Influential Data Points • Points that are outliers in the y direction have large regression residuals. • Other outliers need not have large residuals.

  8. Outliers & Influential Data Points • An observation is influential if removing it would markedly change the result of the regression. • Outliers in the x direction of a scatterplot are often influential in least-squares regression.

  9. Cautions: Regression & Correlation • Correlation measures only linear association. • Extrapolation often produces unreliable predictions. • Correlation and least-squares regression are not resistant. • Lurking variables can make a correlation or regression misleading.

  10. Lurking Variable • A lurking variable is a variable that is not among the explanatory and response variables, yet may influence the interpretation of the relationships among those variables. • Association does not imply causation! • A lurking variable may have a cause-and-effect relationship with the x and y variables, creating a strong association between x and y.

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