 Hello and welcome to the session. In this session, we will discuss a question which says that find the equations of the lines of regression on the basis of the given data. And this data is given to us. And in this data, the different values of x are 10, 12, 14, 15, 16 and 17. And for these values of x, the corresponding values of y are 2, 3, 4, 6, 7 and 8. Now before starting the solution of this question, we should know some results. And that are the regression equation of y on x is given by y values y bar is equal to b value x into x minus x bar the whole. Where y bar is the mean value of y, x bar is the mean value of the regression coefficient of y of x. Where b bar x is given by the formula xy minus summation x into summation y over n whole upon summation minus summation x whole square x and y is given by, equal to bx y into y minus y bar the whole is given by the formula into summation y by n is summation y whole square. Now these results will work out as a key idea for solving out. And now we will start with the solution. We will draw a table for this given data. So we have drawn a table for the given data. We have written different values of x. In the second column, different values of y. Then in the next column, we will find x square. In the next column, we will find y square. We will square the different values of x. Now where x is 10? So x square will be 100. Y square is 145. 40 square is 196. 12 values of y. Now where x is 49 and 8 square is 36. 14 into 4 will be 56. 15 into 6 will be 19. Summation x is equal to, we are getting summation y is equal to 30. Summation x square is equal to 1210. We are getting summation y square is equal to 178. We get summation xy is equal to x bar. Which is by number of observations which are n. So here summation x is 84. Number of observations are 1, 2, 3, 4 of y is given by y bar. Which is equal to summation y over n. And summation y is equal to x by n. Which is equal to 40 over n. Which is equal to the equations of the lines of regression. The regression coefficients. This results we will find the regression coefficient of y on x coefficient. Equal to summation xy minus summation x into summation y. Now summation xy is 450. Summation x is 84. Summation y is 30. 1210. So what do we have these values here? This will be 84 into 30 450 minus minus 1176. Which is further equal to. Which is equal to the regression coefficient by x is equal to 15 by 17. Now using this result which is given in the key idea. The regression equation of y on x is given by. y minus y bar is equal to b minus bar the whole. 14. y bar is 5. And b minus. So putting value values here this implies. y minus 5 is equal to 15 by 17 is 14 the whole. On class multiplying this implies. 17 bar is equal to 15x minus 210. Minus 15x plus 125 is equal to 0. This is the regression equation. Now using this result which is given in the key idea. Now the regression coefficient bxy is given by the formula. Summation x bar minus summation x into summation y by n. Minus summation y whole square that will be equal to. Now summation x is 84 into summation y is 30 is 178 minus summation y is 30 by 28 bxy is equal to 15 by 14. And now the regression on y is given by into bxy into y minus y bar the whole. Now x bar is 14 y bar is 5 and bxy is 15 by 40. This implies x minus 14 is equal to 15 by 14 into y minus 5 the whole. x minus 196 is equal to 15 y minus 75. Now the regression equation hence the equations of lines of regression is equal to 0 minus 25 is equal to 0. This is the given question and that's all for this session. Hope you all have enjoyed this session.