 So we talked about what is correlation? What are the characteristics of the correlation? What are the uses of it? Why when we use it? Now, how we calculate it? The most important question. The most common correlation method we used to calculate the correlation coefficient is the PSN correlation, which is also called PSN product moment correlation, which measures the degree of straight line relationship. We talked about an art that we denote and the PSN correlation when we calculate it, that tells us the degree of the relationship, the direction of the relationship, and then the linearity of the relationship. So mainly, the PSN product moment calculates its linear relationship and also tells us its strength and magnitude and also tells us its direction. So the formula for calculating it is like this, mainly what we are trying to see, we are trying to find out the variability of the two scores. For example, if my score is 1, 2, 3, 4 on x and 5, 10, 15, 20 on y, that means variability not only co-variability of x and y, but also variability within x variable and then within y variable. So when we take the variability, we take its product, that actually tells us the strength of that relationship. So mainly, the correlation formulae, what does it calculate? It calculates the degree to which x and y vary together, like if x is 1, then y is 5, if x is 2, then y is 10. So how they are varying together and then divided by degree to which x and y vary separately. We will see this numerically, notation-wise as well, but you have to remember that the basic assumption is to remove that we will see how to vary x and y and how the variation in x and y varies. So when there is a perfect linear relationship, every change in the x variable is accompanied by a corresponding change in the y variable. We already talked about that if x has a change, if it is perfectly linear, then the corresponding change in x is accompanied by a corresponding change accordingly. Sir, one point increase in x variable, if it is perfectly related, then one point change in y variable will come. In this case, the co-variability x and y together is identical to the variability of x and y separately. That is, if x is 1, then y is 5, if x is 2, then y is 10. So there is a perfect linear relationship between them. Not only are we seeing their co-variability, but we are also seeing that in x and y, the variability is also coming with the same consistency. So the formula and the product if we apply it, then our correlation will be there. The perfect correlation will come and the perfect correlation will be 1. So the maximum correlation we have talked about is from 0 to 1. When there is no linear relationship, a change in the x variable does not correspond to any predictable change in the y variable. For example, we have just talked about 1, 2, 3, 4. And here we have 5, 10, 15, 20. So our 1 is 5, 2 is 10, 3 is 4, y is 15, 4 is 4, y is 20. So this is the perfect linear relationship. But if our relationship is not perfect, this means that we cannot predict the y from one variable. Then we cannot see a predictable change in it. Because if x is 5, then y is 1. But for this variable, if x is 1, then y is here. So the more the variability, our prediction will be the same as before. The less the variability, our prediction will be the same as before. To calculate the Pearson correlation, it is necessary to know about the sum of the products of the deviation. So we have to calculate sp in the formula. We have to calculate the co-variability of x and y. How much is the co-variability of both of them? The sp measures the amount of co-variability between x and y. So the computational formula for the correlation coefficient using product moment correlation method would be summation xy minus summation x, summation y divided by n. And this will only take out sp. If we take out sp, then we can take out correlation coefficient. In the next module, we will be calculating Pearson product moment correlation manually.