Lecture 9

Definition( Regression analysis )is a mathematical measure of the average relationship between two or more variables in terms of the original units of the data.
In regression analysis there are two types of variables:
The variable whose value is influenced or is to be predicted is called dependent variable , also known as regressed or explained variable.
and the variable which influences the values or is used for prediction. is called independent variable , is also known as regressor or predictor or explanatory variable.
Lines of Regression. If the variables in a bivariate distribution are related. we will find that the points in the scatter diagram will cluster round some curve called the "curve of regression".
If the curve is a straight line. it is called the line of regression and there is said to be linear regression between two variables.
The line of regression is the line which gives the best estimate to the value of one variable for any specific value of the other variable. Thus the line of regression is the line of "best /it" and is obtained by the principles of least squares.
Let us suppose that in the bivariate distribution
(X_i.Y_i ); i = 1,2 ,...,n; Yis dependent variable and X is independent variable.