Elementary Statistics and Computer Application

Regression

• Regression is the functional relationship between two variables and of the two variables one may represent cause and the other may represent effect. The variable representing cause is known as independent variable and is denoted by X. The variable X is also known as predictor variable or repressor. The variable representing effect is known as dependent variable and is denoted by Y. Y is also known as predicted variable. The relationship between the dependent and the independent variable may be expressed as a function and such functional relationship is termed as regression.


• When there are only two variables the functional relationship is known as simple regression and if the relation between the two variables is a straight line I is known a simple linear regression. When there are more than two variables and one of the variables is dependent upon others, the functional relationship is known as multiple regression. The regression line is of the form y=a+bx where a is a constant or intercept and b is the regression coefficient or the slope. The values of ‘a’ and ‘b’ can be calculated by using the method of least squares. An alternate method of calculating the values of a and b are by using the formula:
• The regression equation of y on x is given by y = a + bx
• The regression coefficient of y on x is given by


and

• The regression line indicates the average value of the dependent variable Y associated with a particular value of independent variable X.