Page 190 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes
10 × − 5900 60000 −1000
= 2 = = – 0.116
10 × ( − 9860 )300 8600

Regression of Y on X
( YY = YX ( b X ) − X
) −

or (Y – 30) = – 0.042 (X – 20) or Y = 30 – 0.042X + 0.84
or Y + 0.042X = 30.84

Regression of X on Y
( − X = XY ( b YY ) −
) X
or (X – 20) = – 0.116 (Y – 30) or X = 20 – 0.116Y + 3.48
or X + 0.116Y = 23.48

Statistical methods used to answer such questions are the subject matter of regression
analysis. The regression analysis is concerned with the formulation and determination of
algebraic expressions for the relationship between the two variables.

Properties of the Regression Lines
1. The regression lines of Y on X is used to estimate or predict the best value (in least squares sense)
of Y for a given value of the variable X. Here Y is dependent and X is an independent variable.
2. The regression line of X on Y is used to estimate to best value of X for a given value of the
variable Y. Here X is dependent and Y is an independent variable.

3. The two lines of regression cut each other at the points ( ) X,Y . Thus, on solving the two lines of
regression, we get the values of means of the variables in the bivariate distribution.
4. In a bivariate study, there are two lines of regression. However, in case of perfect correlation that is
when r = + 1 on – 1 we have only one regression line as both the regression lines coincide in this case.
5. When r = 0, i.e., if correlation exists between X and Y, the two lines of regression become
perpendicular to each other.
Self-Assessment
1. Which of the following statements is true or false :
(i) The term ‘regression’ was first used by Karl Pearson in the year 1900.
(ii) Regression analysis reveals average relationship between two variables.
(iii) The regression line cut each other at the point of average of X and Y.
(iv) In regression analysis b stand for regression coefficient of X on Y.
xy
(v) The regression line of Y on X minimises total of the squares of the vertical deviations.
12.3 Summary

• We use the general form ‘regression lines’ for these algebraic expressions. These regression lines or the
exact algebraic forms of the relationship are then used for predicting the value of one variable from that of
the other. Here, the variable whose value is to be predicted is called dependent or explained variable
and the variable used for prediction is called independent or explanatory variable.

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