Interpreting a simple regression equation in psychology

Students of psychology know that independent and dependent variables are at the heart of psychological research. Dependent variables are those for the measurement of which psychologists undertake research. Examples include levels of anxiety, body weight, span of attention, degree of extraversion, etc. Independent variables are those which influence these dependent variables. For example, public speaking increases levels of anxiety, stress increases body weight, noise decreases span of attention, socializing increases degree of extraversion, etc. Therefore, public speaking, stress, noise and socializing in these cases are independent variables.

Regression quantifies relationships between independent and dependent variables. As a psychologist does it suffice you to know that stress increases a person's body weight? Wouldn't you need to know by how much the weight increases? Wouldn't you need to know whether the influence is considerable or not? Regression helps you do just this. It gives you a numerical estimate of the influence that an independent variable has on a dependent variable, which is useful in not only a precise understanding of the impact of the independent variable on the dependent variable but which also makes possible further calculations of the impact of other independent variables on the dependent variable, the combined influence of various independent variables on the dependent variable and so forth. 

Take note that in the terminology of regression, an independent variable is referred to as a predictor variable and a dependent variable is known as an outcome variable.

Let's take a sample regression equation for illustration now:

y = 47 + 1.8x

Where, y = body weight;

             x = amount of stress

What does this equation tell us? Let's understand closely:

Assume that we have conducted a study of a hundred participants. We have measured their body weight using a digital weighing scale in kilograms. We have measured their stress levels by making a physiological measurement of their autonomic activity with output on a continuous scale of 1 to 10. After a considered, detailed set of calculations (a demonstration of which is beyond the scope of this post) we arrive at the equation above for the relationship between the predictor variable - amount of stress and the outcome variable - body weight. Now, with the help of this equation, I want to be able to calculate the body weight of any individual in the population from which I had drawn my sample, in future. But what is the equation telling me?

This equation is telling me that for any individual in the population, I can take 47 kg as the base weight and add to it the amount of stress that the person is experiencing multiplied by the coefficient 1.8 to get his exact weight. Say, for instance that I target an individual in the population and measure his stress physiologically using the same procedure that I did with my sample. His stress score turns out to be 5.4. Now, I will substitute this value in the above equation as follows - 

y = 47 + (1.8 x 5.4) = 56.72

I now know that the weight of the person is 56.72 kg, with a contribution of 9.72 kg made by the amount of stress the person has.

How did I arrive at 47 kg as the base weight and 1.8 kg as the contribution of every 1 point of stress? Keeping calculations aside, we need to understand that in the absence of an independent variable of interest, a person obviously has some body weight which is a result of other factors such as food intake, muscle mass, volume of fat quantity, bone density and several more genetic and environmental variables. So the 47 kg simply represents the body weight an individual has anyway, without consideration of stress. The 1.8 kg is the contribution of every 1 unit increase in stress as measured by the physiological measurement of the autonomic nervous system that we have adopted. 

From your study of mathematics, you would recall that every regression equation has a slope and an intercept. The 47 kg is that intercept in this case, the constant of y, the value of y when x is 0. The 1.8 is the slope in this case, the increase in the value of y with an increase in the value of x.

I know that at this point, may questions must be propping up in your head - 

What about the form of the equation we see in our textbooks - y = a + bx + e? What does the 'e' stand for?

Can regression equations also be checked for significance?

How does regression relate with correlation?

There is so much more to explore with regression! Let me know what else you are interested in exploring about this statistical technique in the comments below. For any help that you need with regression and other statistics for your studies, you can contact me on 9892507785 or mail me at jyotikapsychology@gmail.com. I am a home tutor for psychology students of all boards and universities in Mumbai.