extreme values can misleadingly improve R squared

• R squared dependency on sample’s mean makes it susceptible to extreme values (e.g. outliers) when measuring for linear regression or correlation

  • This is because Pearson’s R measure distances of data points from its x-mean and y-mean – linearity and homoscedasticity assumption is critical
  • 
  • Formula to find the Pearson correlation coefficient, denoted as R
    • \[R_{xy}=\frac {\sum\limits_{i=1}^n(x_i-\bar{x})(y_i-\bar{y})} { \sqrt{\sum\limits_{i=i}^{n}(x_i-\bar{x})^2 } \sqrt{\sum\limits_{i=i}^{n}(y_i-\bar{y})^2 } }\]
  • In the case where you do have outliers, the resultant R including them may mislead by either reducing the strength (when the outlier is off tangent), or improve it greatly (when outlier within the line but far off)
    • 

References

• Pearson Correlation Coefficient - Statology
• Pearson Coefficient of Correlation Explained / by Joseph Magiya / Towards Data Science

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• topic:: 00 Statistics00 Statistics
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