State properties of regression coefficient. Also state the point throu

1.	State properties of regression coefficient. Also state the point through which a regression line always passes.
Answer» The properties of regression coefficient are as follows : The signs of correlation coefficient r and regression coefficient b are same. Value of regression coefficient b is independent of change of origin but not of scale. From regression coefficient the estimated change in the value of Y, per unit change in the value of X can be known. The value of b can be less than 1 or greater than 1. The regression coefficient is a relative measure. Sign of ‘b’ depends on the sign of Cov(x, y). If b > 0, a unit increase in X, implies an estimated increase of b units in Y. If b < 0, a unit increase in X, implies an estimated decrease of b units in Y.

State properties of regression coefficient. Also state the point through which a regression line always passes.

Answer»

The properties of regression coefficient are as follows :

The signs of correlation coefficient r and regression coefficient b are same.
Value of regression coefficient b is independent of change of origin but not of scale.
From regression coefficient the estimated change in the value of Y, per unit change in the value of X can be known.
The value of b can be less than 1 or greater than 1.
The regression coefficient is a relative measure.
Sign of ‘b’ depends on the sign of Cov(x, y).
If b > 0, a unit increase in X, implies an estimated increase of b units in Y.
If b < 0, a unit increase in X, implies an estimated decrease of b units in Y.