 Hello and welcome to the session. In this session we will discuss a question which says that equations of two regression lines are 5x plus 8y is equal to 17 and 8x plus 5y is equal to 50. Find first path regression coefficients byx and bxy, second path combination coefficient between x and y. Now before starting the solution of this question we should know some results. First is for the regression equation that is y is equal to mx plus c the coefficient of x, the regression coefficient that is given by bxyx that is coefficient of x is m, so here the regression coefficient of y on x is m which is denoted by byx. Call the regression coefficient of y on x an equation that is the coefficient of y the regression coefficient of x and y that is bxy the coefficient of y where are the correlation coefficient is less than equal to r is less than equal to 1. That is when you add to 1. Now these results will work out as a key idea for solving a problem with the solution. Now the two regression lines are given that are first plus 8y is equal to 75y is equal to 50. Number one and this will be equation number two. Now let equation number one be the regression line that whether our assumption is correct or not. Now we have assumed that the equation one is the regression line equal to minus 8y plus 70 which implies x is equal to minus 8 by 5y plus 70 by 5. Now using this result which is given as the key idea the regression line will be bxy and this is equal to coefficient of y which is equal to minus now we have assumed as the regression line is equal to minus 8x plus this y is equal to minus 8 by 5x plus 50 by 5. Now using this result which is given as the key idea coefficient of regression of y and x that is bxy is equal to x in this equation which is minus 8 by 5. Therefore bxy is equal to minus 8 by 5 is given as the key idea bxy into bxy which further equals minus 8 by 5 into minus 8 by 5x to 4 by 25. And negative therefore also negative is equal to this one the value of bxy and bxy so if both are negative then the negative value of r which is minus 8 by 5 plus then minus 1 b. Now we have assumed that equation one is the regression line of x and y and equation two is the regression line of y and the equation one is the regression line of y and x. The regression line therefore is the regression line so again equal to minus 5x plus 70 which implies y is equal to minus 5 by 8x plus 70 by 8 that is this is the regression line of y and x. Therefore the regression coefficient will be equal to so from equation two equal to minus 5x plus 50 which implies 5 by 8y plus 50 by 8. Now the regression coefficient of x and y that is this equation which is equal to now bxy this implies r square is equal to minus 5 by 8 25 by 64 which further equals r is equal to plus minus 5 by 8. Now as r negative these are negative consider the negative sign and here r is lying between minus 1 and bxy is equal to minus 5 by 8. The regression coefficient p by x is equal to minus 5 by 8 between that is equal to minus 5 by 8 and that's all for this session hope you all have enjoyed the session.