Lecture 4 notes

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

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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 . (MINITAB will compute r . Use Stat Basic Statistics Correlation... ) 1

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2.5.2 Least Squares ( X 1 , Y 1 ) , . . . . . . , ( X n , Y n ) Suppose Y = response variable X = explanatory variable
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