 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that Find linear regression equation when x bar is equal to 24.31, y bar is equal to 77.83, r is equal to 0.841, sx is equal to 1.732 and sy is equal to 0.785. We know that regression equation y on x is given by y hat is equal to a plus bx where slope b or regression coefficient y on x is given by r into sy upon sx and intercept a is given by y bar minus b into x bar where r is the correlation coefficient sy is standard deviation of y, sx is standard deviation of x, y bar denotes mean of y and x bar is mean of x. With this key idea we proceed to the solution. In this question we have to write linear regression equation and we are given mean of x that is x bar which is equal to 24.31 mean of y that is y bar which is equal to 77.83 coefficient of correlation that is r is given as 0.841 standard deviation of x that is sx is given as 1.732 and standard deviation of y that is sy is given as 0.785. From the key idea we know that regression equation y on x is given by y hat is equal to a plus b into x where slope b or regression coefficient y on x is equal to r into sy upon sx and intercept a is given by y bar minus b into x bar so we find b and a now b is given by the formula r into sy upon sx so we put the values of r sy and sx in this equation and we get b is equal to r that is 0.841 into sy upon sx that is 0.785 upon 1.732 Now using calculator we get the value of b as 0.381 now we find intercept a we know that a is given by y bar minus b into x bar now we will put the values of x bar y bar and b in this equation and we get a is equal to y bar that is 77.83 minus of b into x bar that is 0.381 into 24.31 Now again using calculators we get the value of a as 68.56 we know that regression line is given by y hat is equal to a plus bx Now we have got the values of a and b so regression line is given by y hat is equal to a that is 68.56 plus b into x that is 0.381x Thus the required linear regression equation is given by y hat is equal to 68.56 plus 0.381x which is the required answer This completes our session hope you enjoyed this session