 Hi, and welcome to the session. Let's start off with the following question. The question says, in a correlation analysis, the following values are obtained about the variables x and y. x bar is equal to 36, y bar is equal to 85, sigma x is 11, sigma y is 8, and correlation between x and y is 0.66. Find the equations of the regression lines and estimate the value of y when x is equal to 30. Let us start with the solution to this question. We see that the regression equation of x on y is given by x minus x bar is equal to r into sigma x divided by sigma y into y minus y bar. Therefore, x minus 36 is equal to 0.66 into 11 by 8 multiplied by y minus 85. This implies that x is equal to 36 plus 0.9075y minus 77.35. Sorry, this is 77.135. This implies that x is equal to 0.91y minus 41.135. This is the answer to first part. Now, the regression equation of y on x is y minus y bar is equal to r into sigma y upon sigma x into x minus x bar. This implies that y minus 85 is equal to 0.66 into 8 divided by 11 multiplied by x minus 36. This implies that y is equal to 85 plus 0.48x minus 17.28. This implies that y is equal to 0.48x plus 67.72. This is our answer to the second part. Now, we see that when x is equal to 30, then we put this in the above equation and this implies that y is equal to 0.48 into 30 plus 67.72 and this is equal to 82.12. This is our answer to the last part. So, I hope that you understood the solution and enjoyed the session. Have a good day.