Statistical Methods

Unit 9 - Correlation and regression

9.6.1 Special names of the parameters ‘a’ and ‘b’ and expressions for their variances
There are special names for the parameters ‘a’ and ‘b’. The parameter ‘a’ is called the Y intercept. It is the value Y assumes when X = 0. The parameter ‘b’ is called the regression coefficient and gives the slope of the regression line, i.e., it shows how steep the line is. The regression coefficient indicates the rate of change in the dependent variable(Y) per unit change in the independent variable(X).
The variance of the estimates b and a are respectively given by:



where s_y and s_x, are standard deviations of y and x respectively.