 Hello and welcome to the session. In this session we will discuss linear and non-linear relationship in non-linear data and in family drawer the line of first. Now we will see different types of association between two variables. Now whenever we are given a data we follow four steps to find the relationship. First of all we check the pattern of set of plot, then we find the degree of relationship and then we check the type of relationship and then we check if our plans exist. Now in our earlier session we have discussed the relationship and degree of relationship in two variables and now we will see the type of relationship. Now there are two types of relationships, linear and non-linear. Now a linear relationship is that in which the points on the scatter plot are moving upwards or downwards but almost in a straight line and a non-linear relationship is a relationship in which points on the scatter plot are moving upwards or downwards but not in a straight line rather in the form of a curve. Now in the figure one these are moving upwards so there is a positive relationship and we see that these points almost move in a straight line the relationship is called a positive relationship. In this second figure the points are again moving upwards and showing positive relationship but they are not following a straight line rather linear relationship is called non-linear positive relationship and similarly we have linear negative relationship and non-linear negative relationship. Now let us see how we will check for the outlines. Now I will show the scatter plot which do not fit in the general trend of the data. Now look at this scatter plot are away from all. Now let this be point A and this be point B but here one point is according to the trend lying on the same as the point B is not according to the trend. Now let us discuss line of best fit. Now this type of line is drawn in a linear relationship when almost in a straight line. Now when we have drawn the scatter diagram and we have come to know about the pattern which should have about same number of points above. So here we have drawn line of fit and here we have to pay attention to the closeness of points on either side of the line should follow general trend of the data. That is to most of the data points and here we have drawn a line to show linear relationship. Now look at these two images. Now in image way from the line this is not a correct line of fit. In image 2 we can see all the points are close to the line and are both above and below the line. So this is the correct line. Now let us discuss an example. The table current in miles and number of gallons of gas used in it describe the relationship between the two variables. If the data is linear draw the line of best fit. Do you think line is a good fit for the data set? Why or why not? Now let us start with its solution. For this given data we will draw a, now we know that distance traveled depends on the number of gallons of gas available. A scale of 2 per number of miles data let us draw the scatter plot audit pair 0 0 on the graph. So this is the point which represents the audit pair 0 0 when the next audit pair which represents the audit pair 2.3 75 the other audit pairs also by plotting all the audit pairs we are getting this scatter diagram for the given data. Now in this scatter diagram all the points are moving in upward direction. When we are going to increase in the number of gallons the distance traveled is also increased a positive relationship. Now these points are might be close not too far from each other. So there is a moderate degree of association between the two variables and here all the points for the same trend there is a moderate pervasive relationship between the two variables and it is also clear from the graph that almost all the points are moving upward in a straight line a linear relationship there are no outliers. Now let us draw 0 0 in the table so we start from a region and draw in such a way that all the points are close to the line or lie up. So here we have drawn a line in such a way that all the points are close to the line. Now this line which is drawn because all the points are on the line to the line on either side. So in this session we have learnt about linear and nonlinear relationship and how to draw the line of fit for a bivariate theta and this completes our session. Hope you all have enjoyed the session.