Page 205 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 13: Coefficient of Simple Regression Method

Notes
3.5
Y – 67 = 0.8 (X - 65)
2.5
Y – 67 = 1.12 ( X - 65)
Y – 67 = 1.12 X – 72.8
Y = 1.12 X – 5.8 or Y = – 5.8 + 1.12 X

Regression Line of X on Y

σ x
X- X = ( r ) Y- Y
σ y
X = 65 = 0.571 (Y – 67)
X – 65 = 0.571 Y – 38.257
X = 0.571 Y + 26.743 or X = 26.743 + 0.571 Y
(ii) Best estimate of X when Y = 70 can be obtained from the regression equation of X on Y.
X = 26.743 + 0.571 (70) = 26.743 + 39.97 = 66.713
(iii) When X = 66.713, Y will be
X = 1.12 (66.713) – 5.8 = 74.72 – 5.8 = 68.92.
Self-Assessment

1. Which of the following statements are True or False (T/F):
(i) If both the regression coefficients are negative, the correlation coefficient would be negative.
(ii) The under root of two regression coefficients gives us the value of correlation coefficient.
(iii) Regression coefficients are independent of change of scale and origin.
(iv) Regression coefficient of Y on X measures the change in X corresponding to a unit change
in Y.
(v) The regression coefficient of Y on X is denoted by the symbol bxy.
13.3 Summary

• The statistical tool with the help of which we are in a position to estimate (or predict) the unknown values
of one variable from known values of another variable is called regression. With the help of regression
analysis,* we are in a position to find out the average probable change in one variable given a
certain amount of change in another.
• Regression analysis is a branch of statistical theory that is widely used in almost all the scientific
disciplines. In economics it is the basic technique for measuring or estimating the relationship
among economic variables that constitute the essence of economic theory and economic life.
For example, if we know that two variables, price (X) and demand (Y), are closely related, we
can find out the most probable value of X for a given value of Y or the most probable value of Y
for a given value of X. Similarly, if we know that the amount of tax and the rise in the price of
commodity are closely related, we can find out the expected price for a certain amount of tax
levy. Thus we find that the study of regression is of considerable help to the economists and
businessmen.
• Regression equations are algebraic expressions of the regression lines. Since there are two
regression lines, there are two regression equations–the regression of X on Y is used to describe
the variation in the values of X for given changes in Y and the regression equation of Y on X is
used to describe the variation in the values of Y for given changes in X.
• If the values of the constants ‘a’ and ‘b’ are obtained, the line is completely determined. But the
question is how to obtain these values. The answer is provided by the method of Least Squares

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