Speaker 1: Hey everyone welcome back. So in this video we shall take a look at what is multivariate data analysis or multivariate analysis and what are some of the elements involved in it. So first let's see what is a multivariate data set. So it is a data in which values of several variables are recorded on each unit. So this unit can be a person. So for example you may record several variables on a person such as what is a person's height, age, income, education, blood pressure, and so on. Or that unit could be a family right. So what is the average income of the family, the number of people in that family, maybe the average monthly expenditure of the family, and so on. A unit can also be a city, a hospital, a country. Basically it can be anything. It depends upon the research question that you are interested in. So let's see some of the things or some of the studies that involve multivariate data sets. So in several studies in psychology, researchers can collect information on variables such as memory of the subjects or IQ of the subjects. Climate studies is another good example. So a lot of variables such as temperature and rainfall are collected in climate studies. Imaging studies. So we will work a little bit on images in this course. So imaging studies, if you think of each pixel as a separate variable in an image, then these imaging studies could potentially have millions of variables. So maybe you can pause and take a minute to think about an example that would involve hundreds of variables. So multivariate analysis is basically analysis of multivariate data sets. So what are some of the objectives or things involved in multivariate analysis? So one is data reduction. So this basically means to represent the phenomenon under study as simply as possible without loss of any information or with as little loss of information as possible. So one of the techniques we will learn about that does this is PCA or principal component analysis. So one example of this is GDP or the gross domestic product. So this is a function of a lot of variables that indicate the health or financial health of a country. A simpler example is your final grade. So we are combining a lot of different variables such as grades in the different courses that you enroll in to come up with a final measure of your grade. An example related to health. So you can collect several variables related to a cancer patient's response to radiotherapy. And then you could combine all of this information to conclude how well the radiotherapy treatment is working for that particular patient. Another popular objective in multivariate analysis is grouping. So grouping is basically you form groups of similar objects. So we will also spend a considerable amount of time in this course studying different grouping or clustering methods. So we can use these clustering and grouping methods to differentiate between alcoholics and non-alcoholics. So basically we would collect information on various physiological variables on the subjects and then try to differentiate them into these two categories. Grouping is used a lot in marketing to identify different groups of customer, different groups in the customer base. Another objective is to investigate relationship among variables. So if you're going to collect information on several variables, then is there any relationship between them? If yes, then what is the nature of this relationship? So you can think of linear models. In linear regression, you're doing exactly this. We are studying if there is any relationship between the response and the predictor variables. So some of the applications of this could be to study whether there is any relation between risk-taking behavior and performance of top level business executives. Or maybe we want to see if there is any relation between income of parents and the income of their children. So we will not be spending a whole lot of time or we will probably not spend any time on this. But this is an important part of multivariate analysis and just something to keep in mind. Then we come to prediction. So if there is a relation between the different variables that you have, then can you use this relation to predict values of a variable of interest? So prediction is a very, very important problem. So can we predict success of a student in college based on the student's test scores from high school? Or can we predict whether a person will get cancer using different genetic and environmental variables? So you can see that this is a very important question. Again, we will not spend time on prediction in this course. But you can see that this is a very important problem. It involves many, many variables. So this is also a multivariate analysis problem. So next is hypothesis construction and testing. So this is basically we want to test a certain hypothesis of interest. For example, are levels of pollution for a large city constant throughout the week? So maybe it's possible that in a city like New York, the pollution levels are high during the week but are low during the weekend. So is that true? Does the data follow normal distribution? So in many of the different statistical techniques you study, it is possible that a basic requirement for that method is that the data should be normally distributed, right? So if your method is based on this assumption, then when you collect the data, how do you know it is normally distributed, right? Can we test if the data follows a normal distribution? Oh, and then another important one. This is C here. This should have been on the next line. So is the treatment effective, right? So if you have some kind of a treatment for some particular condition, right? Or if you have a drug for something, does the drug, does the medicine work? Is the treatment effective? So this is again an important question. We may study this a little bit in this course, but the focus is going to be mainly on dimension reduction and unclustering methods. So this is all for this video. So in the next video, we shall take a look at what is a population and sample and how do they compare with each other or what are the differences between the two. Bye.