{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Measures of relative standing l median relies on

Info iconThis preview shows pages 15–24. Sign up to view the full content.

View Full Document Right Arrow Icon
Measures of relative standing l Median relies on ranking of data to measure location l Can generalize this notion to percentiles l P th percentile is the value for which P percent of observations are less than that value l Median is the 50th percentile l 25th & 75th percentiles called lower & upper quartiles l Difference between upper & lower quartiles called the inter-quartile range - another measure of spread
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
16 Measures of relative standing… l Simple example l Denote 25th, 50th & 75th percentiles by Q1, Q2 & Q3 l Suppose n = 8, & ordered data are x1, x2, x3, x4, x5, x6, x7, x8 l Need to divide data into quarters l Thus Q1= (x2+x3)/2, Q2= (x4+x5)/2, Q3= (x6+x7)/2 l IQR = Q3 – Q1 l See Keller Ex 4.11 for another example
Background image of page 16
17 Measures of association l Do large values of x tend to be associated with large values of y ? l Graphical answer from scatter plots l Covariance is a numerical measure l Positive (negative) covariance  positive (negative) linear association l Zero covariance  no linear association ( 29 ( 29 ( 29 ( 29 1 covariance Sample covariance Population 1 1 n- y y x x s N y x n i i i xy N i y i x i xy = = - - = - - = μ μ σ
Background image of page 17

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
18 Measures of association… l Covariance is not scale free l Is covariance of 500 big? l Covariance between height & weight depends on units used l Correlation coefficient is standardized measure of association that is unit- free l 1 (-1)  perfect positive (negative) linear relationship 1 1 and 1 1 n correlatio Sample n correlatio Population y x - - = = r s s s r y x xy xy ρ σ σ σ ρ
Background image of page 18
19 Correlations in each of these scatter plots? (Keller Fig. 3.13)
Background image of page 19

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
20 Least squares: The problem l Have ( y i, x i) pairs for i = 1, … , n l Portrayed graphically in scatter plot l Interested in linear relationship between y & x l How do you determine the intercept & slope in this relationship? l Choose values that give the best fit l What do you mean best fit? l One approach is minimize residual sum of squares l Method called least squares l Basis of regression analysis (see Keller Ch 16)
Background image of page 20
21 Least squares: The diagram x b b y 1 0 ˆ + = y x w w w w b 0 e 1
Background image of page 21

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
22 Least squares: The optimization problem squares of sum residual the minimize that estimates slope and intercept be will solution Thus ) ˆ minimize to chosen are & where ˆ Assume 2 1 1 0 1 0 i i n i i i y y ( b b x b b y - + = =
Background image of page 22
23 Least squares: The solution x b y b s s b x xy 1 0 2 1 - = = l Note: l Point of the means will lie on line of best fit l b 1 will have same sign as covariance (correlation) between y & x l Zero covariance (correlation)  b 1 = 0  ?
Background image of page 23

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 24
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}