#21 Multiple Regression Analysis

[Music] Hello and welcome, I am Armin Trust, Professor for Organizational Behavior at the Futtwangen University in Germany. And this is my course on Social Research Methods. [Music] So, hello everybody. Today we talk about another multivariate statistical analysis, another multivariate statistical method, namely the multiple regression analysis. And I suppose this is going to be a rather short one, because what I want to do in this episode is I just want to share with you the fundamental idea behind this analysis and some major concepts related to it. What is it what multiple regression analysis really does? The basic idea here is that you have many or multiple independent variables, not one, many, and you have one dependent variable. That's the idea. So, let me share with you some applications for this. For instance, you might ask yourself when you work in marketing what determines the satisfaction of customers with a particular product. I mean, overall customer satisfaction with a product is of course, I mean we can assume this determined by many, many factors. It might be the design, it might be the functionality, it might be the price, it might be the brand, it might be whatever. And what you ask yourself is to what extent do these different predictors or these different independent variables determine what we get in the end, namely customer satisfaction. What you also could do is you could analyze what determines the salary of people. You can ask employees of various industries, various functions. So, hey, how much do you earn? And then you have a lot of independent variables like responsibility, like age, like profession, education level, like gender, for instance. Maybe some personality traits, like a creableness and the intelligence, or all sorts of things. What you're basically doing before doing a multiple regression analysis is you think of the dependent variable, customer satisfaction, salary, or so. And you think of as many independent variables as somehow you consider as being related to that one independent one. And what you receive at the end is so called beta weights. What is a beta weight? A beta weight tells you to what extent a single independent variable is related to the dependent one. So, in the end you primarily look at the beta weights. So, you can think of the multiple regression analysis as something that is kind of extension of the B-variate regression analysis, which is what we typically name as the correlation. With a correlation you have one independent variable, one dependent variable, and you simply look at the correlation between the two with multiple regression analysis. You understand that? Two, but one dependent many independent variable. So, here is another example in a field where I'm pretty much engaged, namely human resources management, organization, behavior. So, a central question in human resource management is for instance what makes people to leave organization voluntarily. So, we talk about retention or voluntary turnover. And so, why does somebody leave? Why does somebody stay voluntarily with his or her current employer? That's a relevant question because companies are interested in why do people leave? I mean having people voluntarily leaving the organization is not always a good thing. Because you have people who are expert in some fields, you have people in which you have invested a lot of time and effort in their education. And when they leave, that can do harm to the organization. So, you don't want people to leave. Okay, some people you want them to leave. But we talk about voluntary turnover. We talk about people leave the organization against the will of their current employer. And why do people leave? I mean when you have a little brainstorming on that, you might come up with a lot of explanations. You might say, "Wow, maybe because of salary." I mean if you could earn some more in another employer, you leave. But salary is not everything. Maybe work-life balance, maybe something. And I really balance my private life and my work-life in the current job. If not, then maybe I leave and go somewhere else. Maybe I don't have career perspectives in my organization. If I don't see a future in my organization with regards to my personal career, I may leave. Maybe I do not go well with my peers. The mutual relationship with my peers is not so good. Maybe training is something. I don't receive training opportunities in my organization. Maybe I do not like the task. I do. Maybe security. I don't think that this company's stable. I don't think that the company really can give me a safe workplace in the future. Maybe I do not well with my supervisor. I mean you know there's a quote, "People trying companies and leave bosses." So, and this is far from being complete. We could add a lot of other things here. But maybe you do a little study here now and you ask people, "Okay, how do you think about your salary? How do you think about your work-life balance? How do you think about your personal perspectives? How do you think about your peers?" I don't think about it. You just simple scales. How happy are we that? Totally unhappy, completely happy. This is something that you measure in a very little kind of employee survey maybe. And then you add one question. That is related to a person's intention to leave. We name this the flight risk also in practice. So, you might answer the question, "Do you seriously consider leaving the company over the course of the upcoming 12 months? Do you seriously consider leaving the organization over the course of the upcoming 12 months?" So, maybe yes, no. Or to what extent? And we know, or at least at least some evidence that people who say yes to this question have a higher probability of leaving the organization that those who say no. So, the correlation between I say that I have the intention to leave and the actual quitting the job is pretty high. It's pretty high, maybe above 0.7. So, you might not measure actual leaving the organization because of matter of anonymity. But you could ask the question about the intention to leave. It's anonymous. I mean, you could say people still do not say the truth here, but if you do it anonymously and the people trust in the anonymity of the survey, they might give an honest answer on this. So, what you do now is you look at how do these different independent variables, salary, work-life balance, perspective also, how do they relate to the intention to leave to the flight risk? And what you receive then as a result of the multiple regression analysis are the better weights. And then you might find that some better weights are higher than the others. And that tells you that maybe if salary has the highest beta weight, that would tell you that salary is the most important reason why people intend to leave. And if beta is low, say, "Oh, that does not play a role here." So, when we look at those analysis and there are a lot out there, I mean, really in the field of retention, you find a lot of multiple regression analysis. It's a classic in that field. You find contradicting results, as always. But if you look at all those studies, if you do kind of meta study, I would suppose I'm not so sure in this, but from what I see is that Supervisor plays a very, very important role. If you do not well with your Supervisor, that's a strong driver for leaving the organization. And also surprisingly, it's training, but training has a negative weight. It's interesting. So, meaning. If you invest a lot in training in your people, the probability is higher that they leave. This is at least something that you find in many studies. And it might be surprising. Isn't it more obvious that when people receive a lot of training, that they feel committed to the organization because the organization invests a lot in your personal training, that's nice, or a better stay, that's the opposite. It seems to be the opposite. When you attend a lot of training, your capabilities increase. And what you want then is that you you want to apply what you have learned. And if you could not, you changed the organization. Because with every training, your capabilities rise, your market value increases. And if you cannot leverage your increased market value in your organization, you go somewhere else. It's an interesting outcome. Okay. So this is a typical example for for multiple regression analysis. And this whole model with the betas and the independent variable, this is a linear model. It sums up to a total value plus and you have also some error variants, which is not explained through the through the model. And what you do then is the following. You have the real intention to leave. I mean, you have measured it, right? And you have a predicted one based on the model. Okay. So and what the regression analysis now does is it predicts the independent, the dependent variable in our case, flight risk. It predicts it based on the model, based on the better weights and it calculates the dependent variable. So you have the predicted one and you also have the real one. And what you do then is you simply correlate the two. And when you correlate and take it the square, then you have big r square r square and r square is the overall value, which is absolutely important for multiple regression analysis. Because that value tells you to which extent your model that you have found really explains the variance of the data. And this should be as high as possible. You rarely get one, but the closer it goes to one, the better it is. So that's that's basically a multiple regression analysis. Okay. So I would leave it to this for the moment. And next time we talk about multi-dimensional scaling, also a very nice procedure, especially in the social science.