{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lets start with n 0 i 1 yi y xi x sx sy 2 the

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 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 ¯ ¯ − x )(xi − x ) sign(b) sx sx 2 = sx sign(b) /sx sx = sign(b) 2 b2 sx The correlation coefficient is always between The correlation coefficient is always between -1 and 1. Let’s start with n 0≤ i =1 ¯ yi − y ¯ xi − x − sx sy 2 The correlation coefficient is always between -1 and 1. Let’s start with n 0≤ i =1 n = i =1 ¯ yi − y ¯ xi − x − sx sy ¯ xi − x sx 2 n 2 −2 i =1 ¯ ¯ xi − x yi − y + sx sy n i =1 ¯ yi − y sy 2 The correlation coefficient is always between -1 and 1. Let’s start with n 0≤ i =1 n = i =1 ¯ yi − y ¯ xi − x − sx sy ¯ xi − x sx 2 n 2 −2 i =1 ¯ ¯ xi − x yi − y + sx sy n i =1 22 22 = (n − 1)sx /sx − 2(n − 1)rxy + (n − 1)sy /sy ¯ yi − y sy 2 The correlation coefficient is always between -1 and 1. Let’s start with n 0≤ i =1 n = i =1 ¯ yi − y ¯ xi − x − sx sy ¯ xi − x sx 2 n 2 −2 i =1 ¯ ¯ xi − x yi − y + sx sy n i =1 22 22 = (n − 1)sx /sx − 2(n − 1)rxy + (n − 1)sy /sy So, 2(n − 1)rxy ≤ (n − 1)2. ¯ yi − y sy 2 What about the other direction. Let’s start with n 0≤ i =1 n = i =1 ¯ ¯ xi − x yi − y + sx sy ¯ xi − x sx 2 n 2 +2 i =1 ¯ ¯ xi − x yi − y + sx sy n i =1 22 22 = (n − 1)sx /sx + 2(n − 1)rxy + (n − 1)sy /sy So, 2(n − 1)rxy ≥ − (n − 1)2. ¯ yi − y sy 2 Chebechev’s inequality says ¯ The proportion of observations more than t from x is Chebechev’s inequality says ¯ The proportion of observations more than t from x is 2 bounded by sx /t 2 . Chebechev’s inequality says ¯ The proportion of observations more than t from x is 2 bounded by sx /t 2 . 2 sx = 1 n−1 n ¯ (xi − x )2 i =1 Chebechev’s inequality says ¯ The proportion of observations more than t from x is 2 bounded by sx /t 2 . 2 sx = 1 n−1 = 1 n−1 n ¯ (xi − x )2 i =1 ¯ (xi − x )2 + ¯ {i :|xi −x |>t } 1 n−1 ¯ (xi − x )2 ¯ {i :|xi −x |≤t } Chebechev’s inequality says ¯ The proportion of observations more than t from x is 2 b...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online