Biostatistics and Research Methodology - Regression

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MitaliVinodrai

Biostatastics

Education

Deviation method from mean
• Regression equation for X on Y
X- x̄ = bxy (Y-ȳ ), Where bxy is the regression co-
efficient and
bxy=
• Regression equation for Y on X
Y-ȳ ̄ = bxy (X- x̄), Where bxy is the regression
co-efficient and
byx=

Example-1
X Y (X- x
̄ ) (Y- ȳ) (X-x
̄ )2 (Y-ȳ)2 (X- x
̄ ) (Y- ȳ)
2 8 -3 -4 9 16 12
8 12 3 0 9 0 0
6 16 1 4 1 16 4
4 14 -1 2 1 4 -2
5 10 0 -2 0 4 0
ΣX=
25
Σy=
60
Σ(X-x̄)2= 20 Σ(Y- ȳ)=40 Σ(X- x
̄ ) (Y- ȳ) = 14
x̄= 25/= 5 , bxy= 14/40= 0.35
ȳ= 60/5=12 , byx = 14/20= 0.7
X on Y Y on X
x-5= 0.35(y-12) y-12= 0.7 ( x-5)
x= 0.35y- (0.35x12)+5 y= 12+0.7x- (0.7x 5)
x= 0.35 y- 4.2+5 y= 0.7x- 3.5+12
X= 0.35y+0.8 y= 0.7x+8.5

Biostatistics and Research Methodology - Regression

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