bus-stat-book1

The order can also be reversed the frequencies for

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Unformatted text preview: 56 58 60 65 68 70 75 80 85 Y 56 50 48 60 62 64 65 70 74 82 90 80 82 85 90 u = x-A v = y-B u2 v2 uv -20 -14 400 196 280 -10 -20 100 400 200 -9 -22 81 484 198 -7 -10 49 100 70 -5 -8 25 64 40 0 -6 0 36 0 3 -5 9 25 -15 5 0 25 0 0 10 4 100 16 40 15 12 225 144 180 20 20 400 400 400 2 -49 1414 1865 1393 200 nΣuv − (Σu ) (Σv) r= [nΣu 2 − (Σu 2 )] [nΣv 2 − (Σv) 2 ] r= 11 × 1393 - 2 × (-49) (1414 × 11 − (2) 2 ) × (1865 × 11 − (−49) 2 ) 15421 15421 = = = + 0.92 16783.11 15550 × 18114 Correlation of grouped bi-variate data: When the number of observations is very large, the data is classified into two way frequency distribution or correlation table. The class intervals for ‘ y’ are in the column headings and for ‘ x’ in the stubs. The order can also be reversed. The frequencies for each cell of the table are obtained. The formula for calculation of correlation coefficient ‘ r’ is cov( x, y ) Σf ( x − x)( y − y ) r= Where cov(x,y) = N σx, σy Σfxy = −x y N 22 22 Σfx 22 Σfx Σfy 22 Σfy 2 σ 2x 2 = σxx = − xx ; σ yy2y= − ; σ 22 = − yy − N N N N N – total frequency N Σfxy - (Σfx ) (Σfy ) r= [ N Σfx 2 − (Σfx)2 ].[ N Σfy 2 − (Σfy )2 ] Theorem: The correlation coefficient is not affected by change of origin and scale. x− A y−B If u = ; v= t hen rxy =ruv c d Proof: u= x− A c 201 cu = x- A x = cu +A x = cu + A y−B d vd = y – B y = B + vd v= y = [B + v d] σ x = cσ u ; σ y = d σ v cov(x , y ) rxy = σx , σy Σf ( x − x)( y − y ) cov(x,y) = n 1 Σf[(cu+A) - (cu+A)][(dv+B) - (d v+B)] n 1 = Σf cu-cu (dv-d v ) n 1 = Σf c (u - u) d (v − v ) N 1 = Σf cd u - u v − v N 1 = cd Σ f (u − u ) (v - v ) N Σf (u − u ) (v - v ) = cd = cd cov(u, v) N ∴ cov( x, y ) = c.d cov(u, v) cov(x , y ) cd cov(u , v ) cov(u , v ) ∴ r xy = = = = r uv c ..σ u . d .σ v σx σy σu σv ∴ rxy = ruv 202 Steps: 1. Take the step deviations of the variable x and denote these deviations by u. 2. Take the step deviations of t...
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This note was uploaded on 01/18/2014 for the course BUS 100 taught by Professor Moshiri during the Winter '08 term at UC Riverside.

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