 Hello and welcome to the session. In this session we are going to discuss correlation. Correlation is a statistical measure of finding out the degree of association between two or more variables. In other words we can say that when two variables are so related that a change in one is accompanied by a change in the other in such a way that an increase in one is accompanied by an increase or decrease in the other or decrease in one by a decrease or increase in the other. The larger the magnitude of the change in one, the larger the magnitude of the change in the other then the variables are said to be correlated for example a decrease in the price of a commodity is accompanied by an increase in its demand. Now we are going to discuss positive correlation if two variables x and y move in the same direction that is if one increases then the other increases too and vice versa this is called positive or direct correlation. For example if heights of children increase then their weight increase too then we have negative correlation that is if two variables x and y move in opposite direction that is an increase in one corresponds to a decrease in the other and vice versa then the correlation between the two variables is negative or inverse. For example increase in the price of a commodity results in a decrease in its demand. Now we are going to discuss degree of correlation. Correlation between two variables can be perfect or imperfect. Degree of correlation is known by coefficient of correlation which is denoted by r and they are of following types. First is perfect positive correlation when changes in the corresponding values of the two variables are directly proportional that is the two variables vary in the same direction at a constant ratio then it is called perfect positive correlation. In this case the coefficient of correlation r is equal to plus one. For example the circumference and radius of a circle are perfectly positively correlated that is if the value of the circumference increases then the value of the radius will also increase proportionately. Next we have perfect negative correlation that is when the changes in the two variables inversely proportional that is the two variables vary in the opposite direction at a constant ratio then it is called perfect negative correlation and in this case correlation coefficient r is equal to minus one. For example for a constant area of a rectangle there will be perfectly negative correlation between the lengths of its sides. Next to a degree of correlation this is an imperfect correlation where the correlation exists in very large magnitude. The coefficient of correlation ranges between plus 0.70 to plus one for high degree positive correlation which ranges between minus 0.70 to minus one for high degree negative correlation. For example circumference and standard of living have high degree of positive correlation and supply and price of commodity have high degree of negative correlation. Next we have low degree of correlation this is also an imperfect correlation where the correlation exists in very small magnitude. The coefficient of correlation ranges between plus 0.20 to plus 0.40 for low degree positive correlation and that ranges between minus 0.20 to minus 0.40 for low degree negative correlation. Next is moderate degree of correlation then coefficient of correlation ranges between plus 0.40 to plus 0.70 for positive minus 0.40 minus 0.70 for negative moderate degree of correlation has no correlation that is when there is no relation between the variables then there is no correlation between the variables the value of coefficient of correlation is 0. Now we shall discuss methods of studying correlation there are various methods of studying correlation and scatter diagram method is one of those and here we will discuss it. It is a graphical method of finding correlation between two variables for constructing this diagram the H variable or one variable the N independent variable is represented on X axis and this is also known as predicting variable the Y variable or other variable known as the dependent variable the one which is to be predicted is represented on Y axis each pair of X and Y variables are plotted in two dimension space of XY in movement of the pairs of these variables whether they move in the same or in opposite direction now first we have perfect positive and negative correlation if a perfect correlation the points will be on the straight line and if the line slopes upward then it is perfect positive correlation and if the line slopes downward then it is perfect negative correlation in case of perfect positive correlation the coefficient of correlation r is equal to plus 1 and in case of perfect negative correlation the coefficient of correlation r is equal to minus 1 and next we have high degree of negative correlation if the points form a band of some width then there will be imperfect correlation the narrower the band the greater is the degree of correlation that is if the points are close to each other then X and Y have high degree of correlation now if the narrower width band slopes upward then it indicates high degree of positive correlation and if this band slopes downward then it indicates high degree of negative correlation next is low degree positive and negative correlation if the points form a band of greater width then it indicates low degree of correlation and again if this band slopes upward then there is low degree positive correlation and if this band slopes downward then there is low degree of negative correlation now we have low correlation when the points do not form a band that is they are scattered in all directions it indicates that there is no correlation between the variables in this case they are lacking any pattern this is also called video correlation or absence of correlation and here the value of coefficient of correlation r is equal to 0 this completes our session hope you enjoyed this session