# How to interpret multiple regression coefficients [duplicate]

I'm running multiple linear regression with 6 variables. For one of the variables D, the correlation coefficient between D and the response Y is - 0.34. But in the regression output, the coefficient for D is +8.9.

What is the best way to interpret D's influence on Y? Is it safe to assume that there's some confounding going on so I can ignore the fact that the correlation coefficient is negative and thus say increasing D will result in increasing Y?

• I think you will find the information you need in the linked thread. Please read it. If it isn't what you want / you still have a question afterwards, come back here & edit your question to state what you learned & what you still need to know. Then we can provide the information you need without just duplicating material elsewhere that already didn't help you. Commented Sep 20, 2018 at 18:13
• The correlation coefficient r between D and Y summarizes the strength and direction of the relationship between D and Y for all subjects/items in your population represented by the ones in your study. The coefficient of D in the simple regression model relating Y to D only summarizes the same thing. You can compare their signs and they should agree. Commented Sep 20, 2018 at 22:26
• The coefficient of D in the multiple regression model describes a subset of the target population, not the entire population, so it can have a different sign than r. If your model were to include, say, Gender and Age in addition to D, then the coefficient of D in this multiple model describes the strength of the relationship between D and Y among the subset of subjects having the same Age (e.g., 40 years) and the same Gender (e.g., male). That relationship can potentially be different in sign and/or magnitude from the one you would obtain for all subjects regardless of their age and gender. Commented Sep 20, 2018 at 22:28