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

Essay

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