(Requires Appendix Material)Show That the Two Alternative Formulae for the Slope

question 12

Essay

(Requires Appendix material)Show that the two alternative formulae for the slope given
in your textbook are identical. $$\frac { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } X _ { i } Y _ { i } - \bar { X } \bar { Y } } { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } X _ { i } ^ { 2 } - \bar { X } ^ { 2 } } = \frac { \sum _ { i = 1 } ^ { n } \left( X _ { i } - \bar { X } \right) \left( Y _ { i } - \bar { Y } \right) } { \sum _ { i = 1 } ^ { n } \left( X _ { i } - \bar { X } \right) ^ { 2 } }$$

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Definitions:

Different Activities

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Correlation With Causation

The mistaken assumption that a relationship between two variables (correlation) necessarily implies that one causes the other (causation).

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