(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. $$\frac { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } X _ { i } Y _ { i } - \bar { X } \bar { Y } } { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } X _ { i } ^ { 2 } - \bar { X } ^ { 2 } } = \frac { \sum _ { i = 1 } ^ { n } \left( X _ { i } - \bar { X } \right) \left( Y _ { i } - \bar { Y } \right) } { \sum _ { i = 1 } ^ { n } \left( X _ { i } - \bar { X } \right) ^ { 2 } }$$

Recognize the role of the amygdala in distinguishing between friendly and threatening faces.

Comprehend how basic emotions are recognized across different cultures.

Identify the physiological responses triggered by the sympathetic nervous system associated with emotions.

Understand the concept of microexpressions and their relevance to nonverbal cues of deception.

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Definitions:

Pudendal

Relating to the pudendal nerve, which supplies the muscles and skin of the perineum, playing a crucial role in the sensory and motor supply to pelvic area structures.

Genitofemoral

Relating to both genital and femoral (thigh) regions, often referring to a nerve providing sensation and motor function.

Common Fibular (Peroneal)

Relating to the nerve that branches from the sciatic nerve to innervate the lateral part of the shin and foot.

Brachial Plexus

A network of nerves that originates from the spinal cord in the neck and shoulders, providing motor and sensory signals to the upper limbs.