# Thread: Single Negative Beta in Multiple Linear Regression

1. ## Single Negative Beta in Multiple Linear Regression

Hi everyone

I'm having trouble interpreting a single negative regression coefficient in a multiple linear regression. The situation is as follows:

- 16 input variables >> 1 outcome variable
- Individually, all 16 input variables are positively correlated with the outcome variables (all around .45)
- In the multiple regression, 3 of the 16 input variables show significantly positive Betas, 12 seem to have no influence, and one is significantly negative
- Tests for intercollinearity show no problematic values

I don't know how to handle this one negative Beta: On the one hand, its culture variable is positively correlated with the motivation variable (.39). On the other hand, keeping the other 15 input variables constant, it has a negative effect on the outcome variable.

To make a practical example: Let's say we measure how much students like Biology, Math, English, and Sports and compare it to their final overall grade. The correlation between liking a subject and the overall grade is positive for all subjects. But a multiple regression shows positive Betas for Math and English, and a negative Beta for Sports.

How would you explain this?

2. ## Re: Single Negative Beta in Multiple Linear Regression

In a study, it was found that higher income was related to higher death risk
in the following year. After controlling for AGE (age was positively correlated
with income, since e.g. people with more job ecperience etc. tended to earn
more, and higher age also increased mortatlity risk, of course), income was
negatively related to death risk (which wasn't surprising, low income is a
well-know risk factor). So, after controlling for additional variables, the "true"
effect of a certain predictor might emerge. Do a little research for "suppressor
effect".

Kind regards

K.

), income was now

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