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CSS Statistics QUESTION #1998
Question 1
In a simple linear regression of number of breakdowns \((Y)\) on machine age \((X)\), the least squares estimate of slope \(\hat{\beta}\) is given by:
  • \(\dfrac{SS_{xy}}{SS_{xx}}\)✔️
  • \(\dfrac{SS_{xx}}{SS_{xy}}\)
  • \(\dfrac{SS_{yy}}{SS_{xx}}\)
  • \(\dfrac{SS_{xy}}{SS_{yy}}\)
Correct Answer Explanation
The least squares slope estimate is \(\hat{\beta} = \dfrac{SS_{xy}}{SS_{xx}} = \dfrac{\sum(X_i - \bar{X})(Y_i - \bar{Y})}{\sum(X_i - \bar{X})^2}\). The intercept is then \(\hat{\alpha} = \bar{Y} - \hat{\beta}\bar{X}\).