Page 206 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes which states that the line should be drawn through the plotted points in such a manner that the
sum of the squares of the deviation of the actual Y values from the computed Y values is the
least or, in other words, in order to obtain a line which fits the points best ( ∑ c )Y – Y 2 should be
minimum. Such a line is known as the line of ‘best fit’.
• The quantity b in the regression equation is called the regression coefficient. Since there are two
regression equations there are also two regression coefficients–regression coefficient of X on Y
and regression coefficient of Y on X.
• the regression coefficient which may exceed one should also be such in value that when
multiplied by the other coefficient the underroot of the product of the two coefficients does not
exceed one. Also both the regression coefficients will have the same sign, i.e., they will be either
positive or negative. The coefficient of correlation (r) will have the same sign as that of regression
coefficients, i.e., if regression coefficients have a negative sign, r will also have negative sign
and if regression coefficients have a positive sign, r will also have positive sign.
13.4 Key-Words

1. Regression : A statistical measure that attempts to determine the strength of the relationship
between one dependent variable (usually denoted by Y) and a series of other
changing variables (known as independent variables).
13.5 Review Questions

1. What are regression coefficients ? State the properties of regression coefficients
2. What are regression equations ? Explain regression equation of Y on X and X on Y.
3. If one of the regression coefficients is negative what type of variation would you expect in the
original series of pairs of observations ?
4. Give the various properties and characteristics of regression coefficients.
5. If two regression coefficients are 0.8 and 0.6, what would be the coefficient of correlation?
[r = 0.693]
Answers: Self-Assessment

1. (i) T (ii) T (iii)F (iv) F (v) F
13.6 Further Readings

1. Elementary Statistical Methods; SP. Gupta, Sultan Chand & Sons,
New Delhi - 110002.
2. Statistical Methods — An Introductory Text; Jyoti Prasad Medhi, New Age
International Publishers, New Delhi - 110002.
3. Statistics; E. Narayanan Nadar, PHI Learning Private Limied, New Delhi - 110012.
4. Quantitative Methods—Theory and Applications; J.K. Sharma, Macmillan
Publishers India Ltd., New Delhi - 110002.

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