 Hello and welcome to the session. In this session, we will discuss a question which says that from the following data, find the coefficient of correlation and obtain the few regression equations. And this data is given to us. Now before starting the solution of this question, we should know some results. First is the regression equation of y on x is given as y minus yy is equal to b on x into x minus x bar the whole. There, y bar is the mean value of y, x bar is the mean value of x and b on x is the regression coefficient of y on x and b on x is given as summation dx into dy over summation dx square. Where dx is equal to x minus x bar and dy is equal to y minus y bar. That is, dx and dy are the variations of the variables x and y from the arithmetic means of the series. Secondly, the regression equation on y is given as x bar is equal to bxy into y minus y bar the whole. Where is the regression coefficient of x or y and this is equal to summation dx into dy over summation dy square bxy. Where bxy and bxy are regression coefficients. We will work on it as a key idea for solving this question. We will start with the solution. For the given data. So we have made a table for the given data. In the first column, we have written the different values of x. In the second column, the different values of y, the deviation dx which is equal to x minus x bar. Then in the next column, we will find the deviation dy which is equal to y minus y bar. Find dx into dy and dx square. We are getting summation x is equal to 135. And I have added all the values of y. We are getting summation y is equal to 207. Summation x over number of observations. Now here, summation x is 135 over. The number of observations are 1, 2, 3, 4, 5, 6, 7, 8. So the number of observations are 9. So this will be equal to 15. Which is y bar is equal to summation y over number of observations which are n. So this is equal to, now summation y is 207, the deviation dx. This will be equal to x minus x bar and x bar is 15 equal to y minus y bar. So this will be equal to y minus y bar is 23. That is we will subtract 15 from the different values of x. We will get minus 14 is minus 2. 14 minus 15 is minus 1. Next it will be 0. Then it will be 1. Then 2. Then 18 minus 15 is 3 and 19 minus 15 is. Find dy and which is equal to y minus 23. So 13 is 23 will give. 3. 24 minus 23 is 1. Then next it is minus 1. Then minus 2. Then 20 minus 23 is minus 3. Then 19 minus 23 will give. Find dx into minus 4 into 7 is minus 28. Minus 3 into 4 is minus 12. Then this is minus 6. It will be minus 1. 0 into minus 1 is 0. 1 into minus 2 is minus 6. This will give minus 12 and this will give minus 20. Then in the next square that is we will square the different values. 4 minus 1 square is 1. Then next it is 0. Then 1 square 1. 3 square is 9 and 4 square is 7 square the different values of y. Now 7 square is 49. Then it is 16. Then 9. Then 1 square is 1. Then minus 1 square is 1. Minus 2 square is 4. It will give 16 and minus 5 square is 25. Because of dx into dy we are getting summation dx into dy is equal to minus 87. Summation dx square is equal to 60 and summation dy square is equal to 130. In equation equations these results which are given in the D-idea the regression coefficient of y of x that is dyx is equal to summation dx into dy over summation dx square. Now summation dx into dy is minus 87 and summation dx square is 6. So this is equal to minus 87 over 60 which is equal to minus 29 over 20. The regression equation of y and x is given by y minus y bar is equal to dy x bar the whole. Y bar is 23. The values here this implies y minus 23 is equal to minus 29 by 20 into x minus 15 the whole. Which further implies on first multiplying 29 minus 460 is equal to minus 2435. Which further is 29 and h 95 is equal to 0. The regression coefficient given by bxy which is equal to summation dx into dy over summation dy square. Now summation dx into dy is minus 87 and summation dy square is 130. So this implies y is equal to minus 87 over 130. The regression equation on y is given as is equal to bxy into y minus y bar the whole. 10 y bar is 23 and this is the value of bxy. The values here this implies is equal to minus 130 minus 23 the whole. This further implies on first multiplying 130x minus 19950 is equal to which further 130x plus 87151 is equal to 0. Now this is the regression equation of correlation. Now using this result which is given in the key idea equal to bxy into bxy. Now this is the value of bxy and bxy 87 by 130. Now putting these values here this implies r square is equal to minus 29 by 20 into minus 87 by 130. Which further implies square is equal to 2523 by 2600 is equal to 0.9704 approximately 0.9851 approximately. Now this on the value of bxy and byxy and byx both are positive then r is also positive and byx both are negative then r is also negative. So we will consider the negative sign here therefore r is equal to minus 0.989851 approximately. So this is the solution of the given question and that's all for this session hope you all have enjoyed this session.