We assume that 2x + 3y - 6 = 0 to be the line of regression of y on x. 2x + 3y - 6 = 0 ⇒ `x = - 3/2y + 3` ⇒ `"bxy" = - 3/2` 5x + 7y - 12 = 0 to be the line of regression of x on y. 5x + 7y - 12 = 0 ⇒ `y = - 5/7x + 12/7` ⇒ `"byx" = - 5/7` Now, r = `sqrt("bxy.byx") = sqrt(15/14)` byx = `(rσ_y)/(σ_x) = - 5/7, "bxy" = (rσ_x)/(σ_y) = - 3/2` ⇒ `(σ_x^2)/(σ_y^2) = (3/2)/(5/7)` ⇒ `(σ_x^2)/(σ_y^2) = 21/10` ⇒ `(σ_x)/(σ_y) = sqrt(21/10)`. What are the two lines of regression?Regression Lines : Regression line is that line which gives the best estimate of dependent variable for any given value of independent variable. If we take the case of two variables X and Y we shall have two regression lines as the regression of X on Y and the regression of Y on X.
How do you find the regression coefficient of X on Y?The regression equation X on Y is X = c + dy is used to estimate value of X when Y is given and a, b, c and d are constant. Y = a + bx can also be interpreted as 'a' is the average value of Y when X is zero. X = c + dy, value c is the average value of X, when Y is zero.
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Two regression lines are 5y - 8x + 17 = 0 and 2y - 5x + 14 = 0 then mean values of x and y are
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