[MUSIC] Now we are going to start discussing the difference between correlation and causality. Remember, in the last video, we understood what is correlation? And how does it measure the linear relationship between two or more metric variables. Now, regression, which measures the causality, is a slightly different concept than correlation. Because under correlation as we discussed, is the linear relationship between two or more metric variables. Whereas in regression, what we do is understand again our linear relations between two or more variables. But here, one or more of these variables have a causal relation with the variable, or the outcome variable. So this is slightly different because you are trying to find out the causal relation rather than just a linear relation. Now, there's a lot of things which we do in marketing which has to deal with regression analysis. For example, when price and promotion sensitivity is measured, and its effects on sales are understood, that's where regression analysis is used. Again, for new product development, when we run a conjoint analysis that's where, again, a regression analysis is used. Again, other examples of regression can be in methods of modeling diffusion of innovations, like how a new product's sales progress over time. That's, again, where you understand using regression analysis. Finally, for understanding preferences of consumers. How does consumers' preferences affect their final purchase behavior? That's where, again, you'll use regression analysis. Regression is usually done the following ways, especially linear regression. So let's say you have a variable y and you have a set of variables, X1, X2, X3, and so on, for which you want to measure the effect on Y And then you have certain errors which are, let's say denote them by E. So basically, your regression or linear regression analysis will be done such a way that Y is a function of your Xs as well as the error terms. Now, what are the different variables which are observed in a regression analysis? The first one is your dependant variable. That is the variable on which you want to understand the effects of the other variables in which you're looking at. So this is the dependent variable, an example can be sales or preferences and so on. The second set of variables which are important when doing a regression analysis are the independent variables. These are the variables which influence the values of the dependent variable or the outcome variable. So again, let's look at example. Let's say prices and promotions are the independent variables. When you are trying to measure the effect on, let's say sales, which is your dependent variable. Now there are certain variables, under regression analysis, which are unobserved, and which you actually estimate. First one, is called regression coefficient. So what is a regression coefficient? Regression coefficient, is the effect which measures the change in the Y, which is a dependent variable, as you go ahead changing the Xs which are your independent variable. And how one unit change in your X affects your Y. The second important unobserved variable are the intercepts, which is what is the value of Y when your X takes the value of 0. That is if there's none of your X is present. That is none of your independent variable is present, what should be the value of your dependent variable. So these are the two different types of unobserved variables which are relevant when running a regression analysis. The third type of unobserved variable is the error term which is the residual error. That is once you take into account all your Xs, that is all your independent variables, is there something missing? That is there might be some measurement errors which might impact your Y which is a dependent variable. So you have to also take into account this error terms when you're running a regression analysis. So basically we talked about the main concepts of regression analysis in this video. In the next video we are going to look at a little bit more depth into what are the different types of analysis which you can do. With your regression coefficient or with the results of our regression analysis. Thank you and looking forward to meeting you in the next video. [MUSIC]