 Hello and welcome to the session. In this session we will discuss a question which says that the ages and heights of children at a playground are given in the table. A part is, draw a scatterplot for this data. B part is, find least square radiation line. And C part is, at what age would you expect children to reach a height of 160 cm? Now before starting the solution of this question, we should know a result. Suppose we are given bicarbonate data, given by the order pairs x1, y1, x2, y2, x3, y3 and so on. Then, least square regression equation, y1, x is given by, y hat is equal to a plus bx, where b is the regression coefficient y1, x. And this regression coefficient b is given by this formula. That is, b is equal to summation of xy minus n into x bar into y bar. And upon summation of x square minus n into xy square, where x bar is mean of x observations, y bar is mean of y observations and n is the number of observations. And intersection A is equal to y bar minus b into x bar. Now this result will work out as a key idea for solving out the given question. Now let us start with the solution of the given question. Now here we are given this table. That is, we are given a bicarbonate data where x represents h and y represents height. First of all, we will draw its standard plot. Now here, on x axis we will represent the ages and on y axis we will represent the heights with suitable scale. Now the first audit pair that we have to plot is the audit pair 396. So this is the point with coordinates 396. Then the next audit pair is 9132. And this is the point with coordinates 9132. Similarly, we will plot all the other audit pairs on this graph. So we have plotted all the audit pairs and we get this scattered plot. So this is the required scattered plot for the given data. Now in the second part we have to find e squared regression line. Now from the key idea we know that e squared regression line y and x is given by y hat is equal to a plus bx. And we have to find the values of a and b by using these results which are given in the key idea. First of all we have to find values of x bar and y bar. Now we know that x bar is equal to summation of x upon n. Now adding all the values of x which are given in the table we get summation x is equal to 3 plus 9 plus 7 plus 4 plus 12 plus 8 plus 6 that is equal to 49. And the number of observations is equal to 1, 2, 3, 4, 5, 6 and 7. So x bar is equal to summation x upon n that is 49 upon 7 which is equal to 7. Similarly adding all the values of y we get summation y is equal to 840. So y bar is equal to summation y upon n that is equal to 840 upon 7 which is equal to 120. Now for finding the value of b we have to find the value of summation of x bar and value of summation of x square. For this we will need two more columns in the given table to find the values of x bar and x square. First of all let us find the values of x bar. Now here you can see 3 into 96 is equal to 288 similarly 9 into 132 is 1188. Then 7 to 124 is equal to 868. 4 into 103 is equal to 412. 12 into 148 is equal to 1776. 8 into 127 is equal to 1016. 6 into 110 is equal to 660. Now adding all these values we get summation xy is equal to 6208. Now in the next column we will find the values of x square. Now where x is equal to 3 so x square will be equal to 3 square that is 9. Similarly 9 square is 81. 7 square is 39. 4 square is 16. 12 square is 144. 8 square is 64. 6 square is 36. Now adding all these values we get summation x square is equal to 399. So we have got all these values. Now we will put all these values in this formula. And we get b is equal to summation xy that is 6208 minus n that is 7 into x bar that is 7 into y bar that is 120. Whole upon summation x square that is 399 minus n that is 7 into x bar square that is 7 square. Therefore this is equal to 6208 minus 5880. Whole upon 399 minus 343. This is equal to 328 upon 56 which is equal to 5.86 approximately. So b is equal to 5.86. Now we know that a is equal to y bar minus b into x bar. So we will put the values of b x bar that is 7 and y bar that is 120 in this formula. So this is equal to 120 minus 5.86 into 7. So this is equal to 120 minus 41.02 which is equal to 78.98. So regression line y on x is given by y hat is equal to a that is 78.98 plus b that is 5.86 into x. Now we have to find h then height is equal to 160 centimeters that is we have to find x then y is equal to 160 centimeters. Now let this be equation 1. So we will put y is equal to 160 in this equation number 1. And we have 160 is equal to 78.98 plus 5.86 into x which implies 160 minus 78.98 is equal to 5.86 into x and this implies 81.02 is equal to 5.86 into x which implies 81.02 upon 5.86 is equal to x. And this gives x is equal to 13.8 which implies x is approximately equal to 14. So by 14 years of age the height will be 160 centimeters. So this is the solution of the given question. That's all for this session. Hope you all have enjoyed the session.