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SSC Statistics QUESTION #2000
Question 1
The standard deviation of errors (standard error of estimate) in simple linear regression with \(n\) observations is computed as:
  • \(s_e = \sqrt{\dfrac{SS_{yy} - \hat{\beta}\,SS_{xy}}{n-1}}\)
  • \(s_e = \sqrt{\dfrac{SS_{yy} - \hat{\beta}\,SS_{xy}}{n-2}}\)✔️
  • \(s_e = \sqrt{\dfrac{SS_{res}}{n}}\)
  • \(s_e = \dfrac{SS_{xy}}{\sqrt{SS_{xx} \cdot SS_{yy}}}\)
Correct Answer Explanation
The residual sum of squares is \(SS_{res} = SS_{yy} - \hat{\beta}\,SS_{xy}\), and it is divided by \(n-2\) (degrees of freedom for error in simple regression, losing one df each for slope and intercept). Thus \(s_e = \sqrt{\dfrac{SS_{yy} - \hat{\beta}\,SS_{xy}}{n-2}}\).