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We get byx = 1
From regression line X on Y,
16X = 9Y-94
r = ± b1 b2
4 Again , byx = r σy
(Since σ Y 2=16, σY = 4 )
σX = 3.
Variance of X = σX2 i.e., 1 = Again byx = =9
cov( x, y )
x 234 cov( x, y )
or cov (x,y) = 9.
1 = Example 10:
Is it possible for two regression lines to be as follows:
Y = -1.5X + 7 , X = 0.6Y + 9 ? Give reasons.
The regression coefficient of Y on X is b1 = byx = -1.5
The regression coefficient of X on Y is b2 = bxy = 0.6
Both the regression coefficients are of different sign, which is a
contrary. So the given equations cannot be regression lines.
In the estimation of regression equation of two variables X
and Y the following results were obtained.
X = 90, Y = 70, n = 10, x2 =6360; y2 = 2860,
xy = 3900 Obtain the two regression equations.
Here, x, y are the deviations from the Arithmetic mean.
b1 = byx =
b2 = bxy = 2
Regression equation of Y on X is
Ye = Y +b1 (X - X )
= 70 + 0.61 (X –90)
= 70 + 0.61 X – 54.90
= 15.1 + 0.61X
235 Regression equation of X on Y is
Xe = X + b2 (Y- Y )
= 90 + 1.36 (Y –70)
= 90 + 1.36 Y – 95.2 = 1.36Y – 5.2
9.7 Uses of Regression Analysis:
1. Regression analysis helps in establishing a functional
relationship between two or more variables.
2. Since most of the problems of economic analysis are based on
cause and effect relationships, the regression analysis is a highly
valuable tool in economic and business research.
3. Regression analysis predicts the values of dependent variables
from the values of independent variables.
4. We can calculate coefficient of correlation ( r) and coefficient of
determination ( r2) with the help of regression coefficients.
5. In statistical analysis of demand curves, supply curves,
production function, cost function, consumption function etc.,
regression analysis is widely used.
9.8 Difference between Correlation and Regression:
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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.
- Winter '08