{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

bus-stat-book1

# The order can also be reversed the frequencies for

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

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online