Explanation of Regression analysis with regression equation and regression line

Meaning of Regression analysis:

It means stepping back and returning to average value. This is propounded by Sir Francis Galton. It is the measure of average relationship between two or more variables in terms of the original units of data.

Yon X

Y=a+bx

Σ Y=Na+bΣ X

Σ XY=ax+bΣ X2

 Xon Y

X=a+bY

Σ X=Na+bΣ Y

Σ XY=aY+bΣ Y2

Using actual mean

Yon X                    byx =Σ XY/Σ X                        this is regression coefficient

                           (Y-Y mean) = byx (X- X mean)   this is regression equation

Xon Y                  bxy =Σ XY/Σ Y                        this is regression coefficient

                           (X-X mean) = byx (Y- Ymean)   this is regression equation

Thus, regression analysis is mathematical measure of the average relationship between two or more variables in terms of original units of the data.

The regression analysis which is confined to the study of only two variables at a time is called simple regression. While the regression analysis which study two or more variables at a time is called multiple regression.

The mathematical equation of regression curve is called regression equation which enables us to study the average change in the value of dependent variable for any given value of independent variable.

If the regression curve is a straight curve, then there is linear regression between variables. In this case, the value of the dependent variable increases by a constant amount for a unit change in the value of independent variable. however, if the curve of regression is not a straight line, the regression is termed as non linear regression.

Regression line is the line which gives best estimate of one variable for any given value of other variable. Line of regression on Yon X is the line which gives the best estimate for the value of Y for any specified value of X. Line of regression on X on Y is the line which gives the best estimate for the value of X for any specified value of Y.

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