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Lecture 4 notes

Lecture 4 notes - 2.5 SUMMARY AND DISPLAY OF...

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Unformatted text preview: 2.5 SUMMARY AND DISPLAY OF MULTIDIMENSIONAL DATA 2.5.1 2-Dimensional Data ( X 1 ,Y 1 ) , ( X 2 ,Y 2 ) ,... ( X n ,Y n ) eg X = height Y = weight X = SAT verbal Y = SAT math Scatter plot. Plot Y versus X . Example: Devore 7e Ed. p.448 (MINITAB: Graph ⇒ Scatterplot... ⇒ Simple) For multiple samples, (e.g. height vs. weight in men and in women) use one scatter plot, but use different symbols or colors for each sample to mark the points on the graph. MINITAB: Graph ⇒ Scatterplot... ⇒ With groups A numerical measure for strength of association between the two variables is the sample correlation coefficient r : (Example: Devore 7e. p.485–488.) r = n ∑ i =1 ( X i- ¯ X )( Y i- ¯ Y ) √ ∑ ( X i- ¯ X ) 2 ∑ ( Y i- ¯ Y ) 2 = 1 n- 1 n ∑ i =1 ‡ X i- ¯ X S x ·‡ Y i- ¯ Y S y · where S 2 x = ∑ ( X i- ¯ X ) 2 / ( n- 1) , S 2 y = ∑ ( Y i- ¯ Y ) 2 / ( n- 1) Note if X i = Y i all i then r = +1 X i =- Y i all i then r =- 1 Can show- 1 ≤ r ≤ 1 ....
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Lecture 4 notes - 2.5 SUMMARY AND DISPLAY OF...

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