 Hello, I welcome you all once again to my channel, Explore Education. I am Dr. Rashmi Singh, Assistant Professor, Department of Education, S.S. Khandan Girls' Duty College, University of Allahabad and after discussing various types of correlation and correlation coefficient, this time I am going to discuss the regression and prediction. It is the last topic of this unit and the lecture will be bilingual mode and it must be useful and it must be beneficial for all of you. So, first of all, introduction, see where we started from, we started with descriptive statistics. I mean, actually, all the studies we are doing now are part of descriptive statistics. Later, a descriptive statistics will be discussed separately, by the way, I shared the difference between descriptive statistics and inferential statistics, I think, you can see from there too. So, we started from the beginning that the statistics are the science of data and all the data in which the statistics tell us about the description of the data, it tells us about the descriptive statistics, i.e. Varananatmak, Sankhiki, right? And in that, we are on the boundary property, then on the boundary property, we were told that how much data is there in the boundary, what is its value, what is its difference, what is its dimension, is it outliers or not? It does not tell me anything about extreme values. So, we needed the measures of variability in which there was a break, there was a change, we read the deviation in which the data that is there is a lot of variation. So, in the data, average deviation, quartile deviation, standard deviation, then we said that fine, we have known about the data, base division, dimension, dimension, floating. We are not able to find out that if we want to study two variables, then we have a correlation to find out if they are related to each other. Then we found out that correlation can be positive or negative or it can be zero. That is, one line will increase. I am recapping all this again and again. Let's say that one line is increasing and the other one is increasing, then it is positive. If it is happening, then it is negative. If there is no dependency on each other, then it is zero correlation. Then we talked about the need for correlation coefficient, that is the strength of correlation. You must know how strong this relationship is. Then we were told that it can be only minus 1 and plus 1. It can be minus 1 only when there is a perfectly negative correlation and plus 1 only when there is a perfectly positive correlation. This means that its value has to be between these two. Still, we are not told anything about correlation coefficient. We are not told anything. He said that there are two variables related to each other or not. But he said that there is a correlation between the cause and the effect. That is, what is the reason and what is the effect on it. For this, we need regression and prediction. So, there was such a background behind it. Correlation coefficient does not reflect cause and effect relationship, it brings two variables. Correlation coefficient tells us that their relationship is so strong. But it does not tell us what is the reason and what is the effect on it. Thus, we cannot predict the value of one variable for a given value of the other variable. That is why we cannot predict the future of one variable. We cannot predict what the effect will be on the other variable. This limitation is removed by regression analysis. This is the limit of the cause and effect relationship. It is removed from regression analysis. Look at everything. Regression, correlation. You have to study it in Hindi. There is no problem. It is a little strange terminology. English terms are easy to understand. You can use it. So, in regression analysis, the relationship between variables are expressed in the form of a mathematical equation. Similarly, in regression analysis, the two variables are expressed by a clock. It is assumed that one variable is the cause and the other is the effect. It is assumed that one is the cause and the other is the effect. This means that one is the cause and the other is the effect. This is the reason. So, this is how it is talked about. And what else are you saying? Regression is a statistical tool which helps understand the relationship between variables and predicts the unknown values of the dependent variable from known values of the independent variable. You are reading two new variables here. We will talk about other types of variables. There are many types of variables. And the most commonly used one is dependent and independent. All your experimental researches are there. The dependent variable means the source which is unfulfilled. And independent which is independent. So, independent is unfulfilled. So, independent is independent. So, independent is independent. So, independent is independent. There is no effect of that. That is the reason for the effect of the dependent variable. The effect of the change. So, in the independent variable, you do some manipulation or some change. And the effect of that is seen on the dependent variable. This is the story of experimental research. So, they are saying that regression is a kind of indication of this. Which helps us to understand the relationship and predict it. We cannot predict the unknown value of the dependent variable. Which we do not know how much it will change. But we can predict that if you change so much in the independent variable, then the dependent variable will change so much. So, who is independent? The name of this series is dependent. And the independent variable changes the dependent because of its own reason. So, independent is not the effect of the dependent variable. It is the effect of the independent variable on the dependent variable. If you understand it this time, then you will not get confused about the independent variable. Now, the concept of regression. We are saying that in regression analysis, we have two types of variables. What we have talked about is dependent. Or we can call it as explained. Or we can call it as independent. Or we can call it as explained nature. By the way, the name of the dependent variable is more popular. As the name suggests, the dependent variable is explained by the independent variable. As the name suggests, the dependent variable is explained by the independent variable. That is, the effect of the dependent variable is explained by the independent variable. That is why it is sometimes called as explained or explained nature. By the way, this is not very popular. In the simplest case of regression analysis, there is one dependent variable and one independent variable. If we talk about the simplest and simplest regression analysis, then there is only one dependent and one independent variable. But there are more complex regression analysis. Where one dependent variable is explained by the number of independent variables. There is one dependent variable, but there are many independent variables. But if we talk about the simple regression analysis, then there is only one nature. Such a case is termed multiple regression. If we take one dependent and many independent variables in this way, then you can call it multiple regression. In advanced regression models, there can be a number of both dependent and independent variables. And if we go to the more advanced regression model, then the variable sign there is more than one and more than the independent one. So, in simple terms, in each and every multiple, one dependent and many independent and in advance, many dependent and many independent. Let's understand the variable again. It is saying that the variables that researchers are trying to explain or predict is called the response variable. See, how many types of names are there? Dependent variable, co-he, response variable is also saying and dependent variable co-he, co-he, explained variable is also saying. Because it depends on another variable. Because dependent variable is not filling the other layer. That's why it is called response. I mean, we are getting this in the form of a prediction. That's why the response variable is also named. The variable that is used to explain or predict the response variable is called the explanatory variable. It is also sometimes called the independent variable. So, we got three names. Either it is called dependent-independent, or explained or explanatory, or response or predictive or predictor variable. Okay? So, it is saying that the order of the variables is very important in regression. When you do regression analysis, then the order of the variables is very important. The explanatory variable or the independent variable always belongs on the x-axis. See, if you make a graph like this, then what is the x-axis? Horizontal axis is x-axis, and vertical axis is y-axis. So, it is saying that you must always take care of this. You cannot make a mistake in this. You cannot change it, that independent variable will always be on the x-axis. Always on the x-axis. And always your response variable or dependent variable will be on the y-axis. Okay? Sorry? Then it is saying that what is the purpose of this? Why did we do regression analysis? In statistical analysis, regression is used to identify the associations between variables occurring in some data. It is saying that when we do the regression analysis, we use regression where we have to find out what is the association between the different variables. It can show both the magnitude of such an association and also determine its statistical significance. That is whether or not the association is likely due to chance. It is saying that in regression, we also get to know that if there is an association between them, then how strong is their balance? And we also get to know whether it is important or not. What does this mean? When you read the test of significance, then you will get to know whether the difference we are seeing or the association we are seeing in data is actually or by chance. That is, you are seeing it because of a truity. If it is seen because of a truity, it means that it is not statistically significant. But if it is statistically significant, it means that the association is actually and not because of chance. And regression is a powerful tool for statistical inference and has also been used to try to predict future outcomes based on past observations. And when we do regression, we believe that it is a very important and very powerful tool for statistical inference. We can take out some inference, we can predict some future outcomes so that we can predict some future outcomes based on past observations. If we apply regression analysis, then with regression, prediction is always connected. Regression and prediction. Because regression is a prediction of some events. That is why both terms work together. And what does regression do? It allows the researcher to predict or explain the variation in one variable based on another variable. That is, the regression analysis and the analysis we do gives the opportunity to see what changes can be made in the second term or what can be changed in the first term. That is why regression and prediction are the same. And what are the characteristics of regression? Regression is a statistical technique that relates a dependent variable to one or more independent variables. That is, it is a technique that relates us and tells us how many independent variables are associated with each other. A regression model is able to show whether changes are observed in the dependent variable are associated with changes in one or more of the explanatory variable. We can also tell this regression model that the difference that we see in the dependent variable is associated with the changes that are going to be in the independent variable. It does this by essentially fitting up best with line and seeing how the data is dispersed around this line. Regression analysis always creates a line on both sides. On the x-axis, you take one variable and take it on the y-axis. And when you plot it, you will see a single straight line. This is how it goes up. It shows such a straight line. That is why we get to know that we can predict how much the data is. In order for regression results to be properly interpreted, several assumptions about the data and the model self must hold. Even if there is some debate about the origins of the name the statistical technique described above most likely was termed regression by Sir Francis Galton in the 19th century to describe the statistical feature of biological data. He is saying that how many people are old, how much is their work. Sir Francis Galton's name you have read many times. In the 19th century, he was removing some biological data and found out that the statistical feature is a regress to some mean level. This means that the tendency is to come to the opposite side. This means that in regression analysis the maximum or the extreme cases are less and the maximum are covered in a major area. That is why it can be said that it regresses to the opposite side. He is saying that in other words while there are shorter and taller people only outliers are very tall and short and most people cluster somewhere around to the average. He is saying that there are very small and very long people are very short and most people are very long. This means that the tendency is to regress to the opposite side. This is the definition of the equation of regression analysis. When we used to read the middle one everyone would know that whenever you are in your course it is not a simple regression. Y is equal to Mx plus C. Y is equal to A plus Bx X is the value of the explanatory variable. This is a simple regression followed by Y. Y hat is the predicted value of the response variable for a given value of X. B is the slope A is the intercept. When you go to the graph when you are in the middle of the course you do not have to ask a lot of questions. Generally, the conceptual question would be write short notes on regression what do you understand by regression analysis when will be regression analysis be used what is the purpose of regression or what is the significance of regression in statistics. So, the answer to all these is the correlation coefficient where it fails to tell what is the root cause and what is the effect. This is achieved in regression analysis where we find which variable is dependent and which is independent variable. As we know you can know the value of a dependent variable for an unknown independent variable. If the independent variable is this much then the value of dependent variable will be this. You can say that you are able to create inference, you are able to create an assumption, you are able to create a future. So, this is our regression and prediction and now the correlation ends here. This is where our regression ends. And in this way, I have shared all the topics of this unit. Those who are afraid of mathematics those who are afraid of questions those who are afraid of equations have a lot of problems but you can accept that you can understand that there is no such difficulty you just have to understand the concept you have to repeat it 6-7 times you have to write its formula many times you have to write it many times you have to write some formula you have to write some formula you can write it with numerical and get the correct answer and if you do that then this paper will be very easy for you because it doesn't have many theories you have to see this too how many other syllabus in other papers how many other syllabus you remember you have to remember small formula and you have to understand the concepts and see how to use these formulas and write the right calculation and you can use that as a key ok so thank you and don't forget to like and subscribe my channel explore education I have covered regression and prediction analysis regression analysis and prediction in this video so join my telegram group too I have done from this it