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CSS Statistics QUESTION #1981
Question 1
In simple linear regression \(\hat{X}_1 = a + b X_3\), the regression coefficient \(b_{13}\) is given by:
  • \(\dfrac{S_{11}}{S_{33}}\)
  • \(\dfrac{S_{13}}{S_{33}}\)✔️
  • \(\dfrac{S_{13}}{S_{11}}\)
  • \(\dfrac{S_{33}}{S_{13}}\)
Correct Answer Explanation
The regression coefficient of \(X_1\) on \(X_3\) is \(b_{13} = \dfrac{\sum(X_1 - \bar{X}_1)(X_3 - \bar{X}_3)}{\sum(X_3 - \bar{X}_3)^2} = \dfrac{S_{13}}{S_{33}}\), where \(S_{13}\) is the corrected sum of cross-products and \(S_{33}\) is the corrected sum of squares of \(X_3\).