 Hello and welcome to this session. In this session we will learn about regression. Now the word regression means the act of returning or going back to the average value. Note that while all tall fathers have tall sons and all short fathers have sharp sons, the average height of sons of tall fathers is less than that of the fathers and the average height of sons of short fathers is greater than that of the fathers. This tendency to regress or go back towards the average of the population was described as regression. Now regression also helps us to predict the value of one variable or the dependent variable from that of the other independent variable. Therefore the statistical method which helps estimate the variable from the known value of the related variable regression Therefore the tendency to regress or you can say the tendency of going back to this value is called regression and the line this tendency a regression line. The regression line to denote that line which gives best possible estimates of the values of one variable for a given values of the other variable. That's why it is called the line of best fit. That is the regression line is also best fit. So we can write a regression. Now let us discuss the method of conflicting. Now in this method we plot the given data diagram to draw a smooth data. So this is called the freehand method of conflicting. But this method is not used in actual practice. This method has a disadvantage that it depends on individual judgment and different observers will obtain different curves and equations. And therefore the decision of the person will affect the result. Now let us discuss the method of least squares. Now the regression lines are also constructed by least square method. Now in this method a regression line is fitted with different points in such a way that the sum of the squares of deviations and values are released from the fitted line. Now from this diagram consider distances d1, d2, d3, d4, dn drawn from each point x1, y1, y4 and so on up to xn, yn. Now these distances will be positive or negative according to whether the points that is these points are below the curve. Now consider the squares of these values and their sum. So consider d1 square plus d2 square plus d3 square plus d4 square plus so on up to dn square. Now the measure of the goodness of fit to the given data is provided by this quantity that is small. The sum of the squares d1 square plus d2 square and so on up to dn square is large when the fit bad. Therefore we can have the given set of the property that d1 square plus d2 square dn square is a best fitting curve. This square sends a regression curve in the square line. Now let us discuss the line of regression. Now a line of regression is the straight line which gives the best fit in the least square sense to the given set of data. Now we learn about the best fitting curve. Now in case when this best fitting curve is a straight line it is called a line of best fit or a line of regression and the regression is said to be linear. Now there are three lines of regression. The first term that is the line of regression of y or if the line of regression is so chosen that the sum of the squares of deviations parallel to the axis of y is minimized then it is called the line of regression of y or x. Where the line ap is so chosen that the sum of the squares of the deviations of y is minimized. That is these deviations such as pors which are parallel to the axis of y this means that these deviations will change in the y coordinate as they remain the same. And for the value of x1 we are writing y that is y1 and y2 which in the y coordinate will give us the deviation p s and similarly we can get other deviations also. For this line ap and it is called the line of regression of y or x and the algebraic form of regression y is equal to that is the coefficient of x represents the regression of y or x. The regression equation is y bar is equal to the coefficient that the sum of the squares of deviations parallel to the axis of x is minimized and it is called the line of regression of x on y. Of deviations parallel to the axis of x is minimized that is these deviations such as p s and some other deviations like p s which are parallel to the x axis will change into the x axis and where the y coordinate is remaining as it is. For this value y1 of y we have deviations which are parallel to the axis of x is minimized of regression of x on y and the algebraic form of the line of regression is the coefficient of x on y that is bxy. Now the regression that is equal to bxy is the regression coefficient is through the point of intersection of the two lines of regression. Now let us discuss the regression lines of regression when plateau line of graph paper coincides when there is a perfect correlation between the two series. See for example 1 and 2 a regression of x on y and y on x is equal to plus 1 that is the coefficient of correlation is equal to plus 1. Downward the coefficient of correlation r is minus 1 between the lines the lesson is the correlation between the two series and that is the versa. Now the angle between the two lines of regression upwards so we can see between the two lines of regression and both of them the high degree negative correlation. The harsh angle between the two lines of regression so it is a low degree between the two lines of regression and both of them slope downward. So this is a low degree negative correlation that is if the two lines of regression cut each other at right angles then there is no correlation between them. So in the seventh part the two lines of regression cut each other at right angles so here r is equal to 0 and there is no correlation between them. If you have learnt about the regression then regression line hope you all have enjoyed the session.