 Hello and welcome to the session. In this session, we will discuss a question which says that is the following statement true. Here reasons, 4x minus 10y is equal to 14 and 21x minus 14y is equal to 56 are respectively the regression equations of y on x. Now before starting the solution of this question, we should know some results. First is the regression equation of y on x is given in the form y is equal to mx plus c where coefficient of x represents the regression coefficient y that is by x. Here the coefficient of x is m so m is the regression coefficient of y on x and it is given by by x. Secondly, the regression equation x and y is x is equal to m y plus c where coefficient of y represents the regression coefficient of x on y that is by. So here the coefficient of y is m so m is the regression coefficient of x and y that is given by bxy. You can say that the slope of the lines in these equations is known as the regression coefficient. Now these results will work out as a key idea for solving out this question. And now we will start with the solution. In the equation we have to check that is this statement true that is these results when the equations of two lines are given to us and we have to find that which one is the line of regression of y on x. Then which is arbitrary as the line of regression of y on x and other as the line of regression of x on y. In the second step of regression that is the regression coefficient of the first step we obtain the result of these regression coefficients and the product of these regression coefficients is equal to a correlation. Equal to 1 these regression coefficients as less than equal to 1 then assumption is correct and assumed bias will be the regression line of y on x. See with the solution of this question here this line is given as the regression equation of x on y as the regression equation of y on x. Now the regression equation y is equal to 14 which implies dividing throughout y2 it will be 2x minus 5y is equal to 7. This further implies 5y plus 7 5 by 2 into y plus 7 by 2. Now using this result which is given in the key idea the regression coefficient which is equal to bxy is equal to the coefficient of y let it be equation number 1 and the coefficient of y here is 5 by 2 bxy is equal to 5 by 2. bxy is equal to the slope of the line 1 and the slope of the line 1 as the regression x minus 14y is equal to 57 by 7 it will be 3x minus 2y is equal to 8. Further this implies which further implies y is equal to 3 by 2 into x minus 8 by 2 and let it be equation number 2. Now using this result which is given in the key idea the regression coefficient of y on x given by bxy is 3 by 2 the slope of the line now to bxy is equal to 5 by 2 x is equal to 3 by 2. So this is equal to 3 by 2 into 5 by 2 which is equal to 59 that given question and that's all for this session hope you all have enjoyed the session.