 Hello and welcome to the session. In this session, we will discuss the question which says that a test about general awareness was conducted on seven students of different classes and the marks scored are observed as follows. That is, this data is given to us in which the students' class is given as 6, 7, 8, 9, 10, 11 and 12 and the corresponding marks scored are 10, 12, 14, 16, 17, 21 and 22. Then first part, find a line of best fit and taking that estimate the general score of a student who is of class 4. Now before starting the solution of this question, we should know some results. First is, now we know that the regression line always passes through the point x mark, y mark, that is the mean. Therefore, the regression equation of y on x is given by y minus y bar is equal to b y into x minus x bar the whole. The x mark is the mean value of x, y bar is the mean value of y and b y x is the regression coefficient of y on x. And b y x is equal to summation dx into dy over summation dx square where dx is equal to x minus x mark and dy is equal to y minus y bar. That is, dx and dy are the deviations of the variable x and y from the infinitive means of the series to determine the line of regression to determine the line. Now these results will work out as a key idea for solving out this question. And now we will start with the solution. First of all, we will draw a table for the given data. So we have drawn a table for the given data. In the first column, we have written the student's class and we are representing it by x. And in the second column, we have written the marks scored and we are representing it by y. And in the next column, we will find dx and dy. And in the next column, dx into dy and the next column, dx square and in the last column, dy square. Now by adding all the values of x, we are writing summation x is equal to, on adding all the values of y, we are getting summation y is equal to 112. Now, which is divided by x by the number of observations which are n, which is equal to, now summation x is 63. And number of observations are 1, this is equal to, that is equal to summation y by n, which is equal to, now summation y is 112. dx is equal to x minus x bar, which will be x minus 9 and dy will be equal to y minus y bar and y bar is, and dx will be x minus minus minus 2. Now h minus 9 is minus 1, 9 minus 9 is 0, 10 minus 9 is 1, 11 minus 9 is 2 minus 9 is different values of y. So, what we will give, minus 2 will give 0 and 22 minus 16 is dx into dy. So, of dx and dy, x will be, h2 will be, to have 0 into 0 is 0, 1 into 1 is 1, in this column. So, where dx is minus 3, so its square will be, where it is minus 2, i is 1, then 0, then 1, then 2 square is 4 and 3 square is 9. And now i am going to have a different values of dy, then minus 6 square is 36, minus 4 is then 0, then 25 and then 36. For values of dx into dy, we have summation dx into dy is equal to 57, summation dx square is equal to 28 and summation dy square is equal to 118. Now in the first part we have to find a line of best fit. Now to determine the line of regulation, we have to determine the line of best fit. By using this result, we should have y on x, y on x is given by minus y bar is equal to dy, which implies y minus y bar is equal to summation dx into dy, we have summation dx x bar the whole. Now x bar is 9, which is 57, 28. So, we can have y bar 28 into x minus 9 the whole. So, in first multiplying this implies 28 y minus 448 is equal to which is, it is given that in the probable score, that means we have to determine the value of y. That is this line, this equation, let it be equation 8, we will put x is equal to 4 into y minus 65 is equal to 0, is equal to 28 y, it is further this, 163 is equal to 28 y and this implies y is therefore y is just an integer, we have the given question and that is all for this session. Hope you all have enjoyed this session.