 Hello and welcome to the session. In this session we will discuss a question which says that find the equation of the regression line of x and y if the observations x and yi are the following. And that are 2, 3, 4, 5, 5, 3, 6, 4, 7, 9, 9, 10, 11, 7, 12, 8. Draw the regression line of x and y. Now before starting the solution of this question we should know some results. And that are the regression equation on y is given by x minus xy is equal to bxy into y minus y bar the whole. Where x bar is the mean value of x, y bar is the mean value of y and bxy is the regression coefficient of x on y. And secondly the regression coefficient bxy is given by the formula summation xy minus summation x into summation y over n whole upon summation y square minus summation y whole square by n. Now these results will work out as a key idea for solving out this question. And now we will start with the solution. Now in regression the various observations are given to us and you have to find the equation of the regression line of x and y. So first of all we will draw a table for these observations. So we have written the observations in this table and here in the first column we have written the various values of x and in the second column corresponding to x we have written various values of y. Now in the next column we will find x square by taking the square of the different values of x and then in the next column we will find y square by taking the square of the different values of y. In the next column we will find xy that means the different values of x into the different values of y. Now let us find x is equal to 2. So x square will be 4, here x is 4, so x square will be 16, 5 square is 25, 6 square is 36, 7 square is 49, 9 square is 81, 11 square is 121, 12 square is 144 y square by scoring different values of y. Now where y is equal to 2 and 2 square is 25, 3 square is 9, 9 square is 81, 10 square is 49, 8 square into y. Now where 2 into 2 will be 4, 5 will be 20, 5 into 3 will be 54 is 24, 7 into 9 is 63. Then 9 into 10 is 90, 11 into 7 is 77 and 12 into 8 is 96. Next we are getting summation x is equal to, we are getting summation y is equal to 48. When adding different values of x square we are getting summation x square is equal to 4 times the values of y square, we are getting summation y square is equal to 348 and we will get summation xy is equal to 389. Now the new value of y which is equal to summation x over the number of observations. Now where summation which is equal to summation y is y bar which is equal to summation y by n which is equal to, now summation y is 48 and x by n which is equal to 7 and y bar is equal to summation y by n which is equal to, which is given as a key idea. The regression coefficient minus summation x into summation y over n. Now summation xy is 389, summation x is 56, summation y is 48, this will be equal to 48 by 8. What happens which is further equal to 389 minus 56 into 48 by 8. 8 into 6 is 48, here also 8 into 6 is 48. So this will be equal to 89 minus 56 into 68, 0.8 is equal to 0.8 which is given as a key idea. The equation line is equal to bxy into y minus y by the whole. bxy is 53 by 67 is equal to 53 by 60 into y minus 6 the whole. Further on cross multiplying x minus 420 is equal to 53 y minus 318. The equation of the regression line which is given by equation number 1. Now for any value of y we can find out the corresponding value of x by this equation into 2 minus 102 is equal to 0, x is equal to plus 102. This further implies x is equal to 200. Now here 2 into 30 is 60, 2 into 104 is 200, into 52 is 104. So this implies x is equal to 52 by 15 which is equal to equation number 1. And we have proved earlier that the point 76 also lies on the line 1. Because the point 3.5 plotted the points and on joining these two points we are getting the required line of regression of x and y. Solution of the given question and that's all for this session. Hope you all have enjoyed the session.