Regression lines

Regression Lines

A line of regression by the method of “least square” shows an average relationship between variables under study. This regression line can be drawn graphically or derived algebraically. A line fitted by method of least square is known as the line of best fit. There are two regression lines:-

Regression line of x on y: Regression line of x on y is used to predict x for a given value of y. The regression equation of x on y is x=a by.

Regression line of y on x: Regression line of y on x is used to predict y for a given value of x. The regression equation of y on x is y=a bx

Two Regression Lines:

We know that there are two lines of regression: - x on y and y on x. For these lines, the sum of the square of the deviations between the given values and their corresponding estimated values obtained from the line is least as compared to other line. One regression line cannot minimise the sum of squares for both the variables that is why we are getting two regression lines.

(We get one regression line when r = 1 and Two regression lines will be at right angles when r = 0.)