Show That the Two Alternative Formulae for the Slope Given

question 44

Essay

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

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Definitions:

Long-term Memory

The phase of memory capable of storing an unlimited amount of information indefinitely, ranging from a few minutes ago to as far back as one can remember.

Theory of Mind

The ability to attribute mental states—beliefs, intents, desires, emotions—to oneself and others and to understand that others have beliefs and desires different from one's own.

Beliefs and Desires

The mental attitudes and inclinations that influence a person's motivations and actions.

Memory Capacity

The amount of information that can be held in a person's memory system at one time.