Derivation 2 sy 1 n1 1 n1 1 n1 b2 n yi y

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Unformatted text preview: )2 i =1 1 n−1 n ¯ (xi − x )2 i =1 Let yi = bxi , then 2 2 sy = b2 sx . Derivation. 2 sy = = = 1 n−1 1 n−1 1 n−1 = b2 n ¯ (yi − y )2 i =1 n ¯ (bxi − bx )2 i =1 n ¯ b2 (xi − x )2 i =1 1 n−1 2 = b 2 sx n ¯ (xi − x )2 i =1 Let yi = byi + a, then rxy = Let yi = byi + a, then rxy = rxy . Let yi = byi + a, then rxy = rxy . Derivation. rxy = 1 n−1 n i =1 (xi ¯ ¯ − x )(yi − y ) sx sy Let yi = byi + a, then rxy = rxy . Derivation. rxy = 1 n−1 = 1 n−1 n i =1 (xi ¯ ¯ − x )(yi − y ) sx sy n ¯ ¯ i =1 (xi − x )([byi + a] − b [y + a]) sx bsy Let yi = byi + a, then rxy = rxy . Derivation. rxy = 1 n−1 = 1 n−1 = 1 n−1 n i =1 (xi ¯ ¯ − x )(yi − y ) sx sy n ¯ ¯ i =1 (xi − x )([byi + a] − b [y + a]) sx bsy n ¯ ¯ i =1 (xi − x )(yi − y ) sx sy Let yi = byi + a, then rxy = rxy . Derivation. rxy = 1 n−1 = 1 n−1 = 1 n−1 = rxy n i =1 (xi ¯ ¯ − x )(yi − y ) sx sy n ¯ ¯ i =1 (xi − x )([byi + a] − b [y + a]) sx bsy n ¯ ¯ i =1 (xi − x )(yi − y ) sx sy Let yi = byi + a, then rxy = rxy . Derivation. rxy = 1 n−1 = 1 n−1 = 1 n−1 = rxy n i =1 (xi ¯ ¯ − x )(yi − y ) sx sy n ¯ ¯ i =1 (xi − x )([byi + a] − b [y + a]) sx bsy n ¯ ¯ i =1 (xi − x )(yi − y ) sx sy Let yi = bxi + a, then rxy = Let yi = bxi + a, then rxy = 1 (or -1, if b is negative). Let yi = bxi + a, then rxy = 1 (or -1, if b is negative). Derivation. rxy = 1 n−1 n i =1 (xi ¯ ¯ − x )(y − y ) sx sy Let yi = bxi + a, then rxy = 1 (or -1, if b is negative). Derivation. rxy = 1 n−1 n i =1 (xi = 1 n−1 n i =1 (xi ¯ ¯ − x )(y − y ) sx sy ¯ ¯ − x )([bxi + a] − [bx + a]) sx 2 b2 sx Let yi = bxi + a, then rxy = 1 (or -1, if b is negative). Derivation. rxy = 1 n−1 n i =1 (xi = 1 n−1 n i =1 (xi = 1 n−1 n i =1 (xi ¯ ¯ − x )(y − y ) sx sy ¯ ¯ − x )([bxi + a] − [bx + a]) sx 2 b2 sx ¯ ¯ − x )(xi − x ) sign(b) sx sx Let yi = bxi + a, then rxy = 1 (or -1, if b is negative). Derivation. rxy = 1 n−1 n i =1 (xi = 1 n−1 n i =1 (xi = 1 n−1 n i =1 (xi ¯ ¯ − x )(y − y ) sx sy ¯ ¯ − x )([bxi + a] − [bx + a]) sx 2 b2 sx ¯ ¯ − x )(xi − x ) sign(b) sx sx 2 = sx sign(b) /sx sx Let yi = bxi + a, then rxy = 1 (or -1, if b is negative). Derivation. rxy = 1 n−...
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This document was uploaded on 03/02/2014 for the course STATS 4150 at Barnard College.

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