Page 345 - DMTH404_STATISTICS

Unit 23: Regression Analysis

5. Regression coefficient in bivariate frequency distribution Notes

é Nåå f u v - f u f v ¢ ) ù
k ij i j (å i i )(å j j
b = ê ú
2
h ê Nå f u - (å f u ) 2 ú
ë i i i i û
6. Standard Error of the estimate

2
s Y X = s Y 1- r for large n ( i.e., n > 30)
.
2 2
Y -
å ( i Y ) ( 1- r )
= for small n
n 2
-
II. Regression of X on Y

å XY nXY n XY - å )( Y )
-
( X å
å
1. Regression Coefficient d = =
2
2
å Y - nY 2 n Y - å ) 2
( Y
å
Cov (X Y, ) s X
= 2 = r×
s Y s Y
2. Change of scale and origin
é ù
X A Y B h n uv - å )( v )
-
-
å
( u å
If u = and v = , then d = ê . ú
2
h h k ê n v - å ) 2 ú
( v
ë å û
3. Constant term c = X - dY
4. Alternative form of regression equation
d Y - i
X = d s Y - d Yi
X - Y or X - X = r. X
C C
s Y
5. Regression coefficient in a bivariate frequency distribution
é ) ù
ij i j
h ê Nåå f u v - (å f u )(å f v ¢ j j ú
i i
d = 2
k ê 2 ) ú
¢
ê Nå f v - (å f v ¢ j j ú
j j
ë û
6. Standard error of the estimate
s X Y = s X 1- r 2 for large n ( i.e., n > 30)
.
2 2
å ( X - X ) ( 1- r )
i
= for small n
n 2
-

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