# Why beta sign is different than correlation sign? [duplicate]

I am trying to interpret the sign of my 5 x-variables against y-variable. The sign of some coefficients in the regression output (command: reg) are different than the signs under correlation matrix (command: correlate). Which one defines the relation sign/direction?

• Can you please add the statements as a code block. Would help in understanding the question better. – Dawny33 Aug 21 '15 at 17:11
• In the regression output under the column Coef, it shows -58.17107 for x1. When I ran correlate command to get the correlation matrix, I get 0.8592 correlation value between x1 and y. This difference in signs is confusing. – Asaad Aug 21 '15 at 17:49
• Do a search on Simpson's Paradox. This is a fairly famous statistical concern. – DWin Aug 21 '15 at 19:02
• This page is a good introduction to these issues in the context of logistic regression; the essential issues in terms of independent variables are the same in linear regression. – EdM Aug 21 '15 at 20:14
• I believe you will get the understanding you need in the linked thread. Please read it. If you still have a question afterwards, come back here & edit your Q to state what you've learned & what you still don't understand. Then we can provide the information you need without simply duplicating material elsewhere that already didn't help you. – gung - Reinstate Monica Aug 21 '15 at 20:40

Consider the following data set where the simple correlation between Y and X1 is positive Let is analyze Y as a function of X1 and X2 . First separately then together. The regression coefficient of the unconditional relationship between Y and M_X1 is .463 ( same sign as the simple correlation ) while the conditional impact of M_X1 given M_X2 is -1.222 (different sign ). As others have pointed out this is sometimes referred to as " the expected sign fallacy ', "Simpson's paradox" , "Ecological fallacy " etc. In summary conditional analysis (multiple regression) is often different from unconditional analysis (simple regression) because the predictor variables are not independent of each other.