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SSC Statistics QUESTION #1999
Question 1
The coefficient of determination \(r^2\) in a simple linear regression is best interpreted as:
  • The slope of the regression line
  • The proportion of total variation in \(Y\) explained by the linear relationship with \(X\)✔️
  • The correlation between residuals and fitted values
  • The ratio \(\dfrac{SS_{xy}}{SS_{xx}}\)
Correct Answer Explanation
\(r^2 = \dfrac{SS_{reg}}{SS_{yy}} = 1 - \dfrac{SS_{res}}{SS_{yy}}\). It represents the fraction of variability in \(Y\) that is accounted for (explained) by the linear regression on \(X\). Values close to 1 indicate a strong linear fit.