 Hello and welcome to the session. In this session we will discuss a question which says that find the line of regression of y on x from the following data. And this data is given to us in which the values of x are given as 3, 4, 6, 7, 9, 10, 11 and the corresponding values of y are 2, 1, 5, 8, 12, 14 and 15. Now before starting the solution of this question we should know some results. First is the regression equation of y on x is given by y minus y bar is equal to b y x into x minus x bar the whole where y bar is the mean value of y, x bar is the mean value of x and b y x is the regression coefficient of y on x. And secondly if the actual mean is in fraction then the deviations are taken and assumed mean that is let u is equal to x minus m and v is equal to y minus b where u and v are the deviations which are taken from the assumed mean and a and b are the assumed means of the two series that is of x series and y series respectively. And the regression coefficient b y x is given by the formula summation u v minus summation u into summation v by n where upon summation u whole square now these results will work out as a key idea for solving out this question. And now we will start with the solution and from the start up r which is equal to summation x by number of observations which are n. Now on origin summation x is 50 and the number of observations are 1, 2, 3, so 50 by 7 will be equal to 7.14. And the mean value of y that is y bar is equal to summation y by n which is equal to summation y will be equal to 57 so this will be equal to 8.14. Now we will use a fraction then the deviations are taken from an assumed mean. Now there are also x bar and y bar are in fractions so well for solving out this question we will take the deviations from the assumed mean. Now we have drawn a table for the given data and written the different values of x in the second column and the values of y 1 in the next column u which is equal to x minus t and in the next column we will find v which is equal to y minus p u into v that is u v and in the next column we will find u square and in the last column we will find v square. So x by n which is equal to 50 by 7 which is equal to 7.14 and y bar is equal to summation y by n which is equal to 57 by 7 which is equal to 8.14. Now as the means are not per number's deviations assumed means. Now let the assumed mean series is equal to 7.14. So we will turn the assumed mean to the nearest whole number so it will be equal to and the assumed mean will be equal to 8 to the nearest whole number so the assumed mean for y series will be 8 this v and v is u that is we will subtract 7 from the different values of n minus 7 which is minus 4 then 4 minus 7 which is minus 3, 6 minus 7 is minus 1, minus 7 is 2, 3, 11 minus 7 is that is we will subtract 8 from the different values of y so 2 minus 8 will be minus 6, 1 minus 8 is minus 7, 5 minus 8 is minus 3, 12 minus 8 is 4, 14 minus 8 is 6. Finding u v we will multiply the different values of u with the different values of v. Now we are minus 4 into minus 6 is 24, minus 3 into minus 7 is 21, minus 1 into minus 3 is 3, 0 into 0 is 0, 2 into 4 is 18, and 4 into 7 is square that is we will square the different values of u. Now minus minus 3 square is 9, minus 1 square is 1, 0 square is 0, 2 square is 4, 3 square is 9 and 4 square is 16. Now for v square we will square the different values of v. Now minus 6 square is 36, minus 7 square is 49, minus 3 square is 9, 0 square is 0, 4 square is 36 and 7 square is 49. Now on adding different values of u we are getting summation u is equal to 1 and on adding different values of v we are getting summation v is equal to 1, we are getting summation u v is equal to 1002 of u square we are getting summation u square is equal to 55 and on adding different values of v square we are getting summation v square is equal to 195. Now using this result which is given in the key idea that is the formula for finding out the regression coefficient of y on x. Now v on x is given by the formula summation u v minus summation u into summation v by n, now summation u v is 102, summation u v is 1, summation v is 1 this will be equal to 101 into 1 by 7 minus 1 square by 7. On taking the same numerator and denominator it will be minus 1 full upon minus 1 full upon 7. Now this is equal to minus 1 is 713 by 7 into minus 1 is 384 to 713 by 384 therefore v by x is equal to 713 equation of y on x, now this is the equation of regression of y on x. Now the regression equation of y on x is y by is equal to b by x into x minus x by the whole. Now x by is 50 by 7, y by is 57 by 7 and b by 384 putting all these values here this implies y minus is equal to 713 by 384 50 by 7 the whole is equal to 713 by 384 7 the whole. Solving and cross multiplying this implies 387 the whole is equal to 713 into 7x minus 50 the whole. And 88y minus 21,888 is equal to 4991x minus which further implies 88y minus 4991x is equal to 0. An equation of y on x, an equation and that's all for this session hope you all have enjoyed this session.