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The below mentioned article provides a study note on regression.
Regression is used to denote the estimation and prediction of the average value of one variable for a specified value of the other variable. This estimation is done by deriving a suitable equation on the basis of available bivariate data. This equation is called Regression equation and its geometrical representation is called Regression curve.
The regression equation requires the Regression coefficient. The regression coefficient (b) is calculated in two different ways.
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The regression coefficient of y on x is:
and the regression coefficient of x on y is:
δy = standard deviation of y
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δx = standard deviation of x
Regression Line:
When the bivariate data are plotted on graph paper, the concentration of points shows certain pattern showing the relationship. When the trend points are found to be linear then by least square method we can obtain the regression line.
If two variables are linearly related then the relation can be expressed as y = bx + a, where ‘b’ is the slope of the line and ‘a’ is the intercept of that line.
If we put the values on regression equation then we can get the regression line equation easily. With the help of Example 1, we can discuss it.
The regression equation of x on y is:
The regression equation of y on x is:
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Significance:
This equation will help us to get the estimate of one variable when the other is given or else we can predict the values of one variable when the other one is also assumed, i.e., extrapolation is possible.
