If your regression coefficients do not seem to make sense, it is quite possible your model is misspecified. For example, it is possible to see the direction of one predictor’s effect change with the addition of another predictor. Such a change in direction may be a sign of "model misspecification". Many different types of modeling issues fall under this umbrella. In the code below, we show the an example of a change in coefficient direction. This model is misspecified because the assumed relationship between variables x1 and y is incorrect.
These regressions include two predictor variables, x1 and x2, that are correlated (rho = 0.55) and an outcome, y, that has a linear relationship with one and a quadratic relationship with the other. In scatter plots, we can see that y is individually positively correlated with both x1 and x2, but the regressions show that the coefficient for x1 changes direction with the inclusion of x2, which we would expect given how we define y. Because these regressions are assuming a linear relationship between y and x1 when, in fact, the relationship is quadratic, the coefficients for x1 are deceptive. Adding a quadratic x1 (or an interaction term, because x1 and x2 are so highly correlated) addresses this issue.
local obs =100 local seed = 12345 clear set obs `obs' set seed `seed' mat a = (1, .55.55, 1) corr2data x1 x2, corr(a) gen e = rnormal() gen y = .1 -.2*x1 + .8*x2 -.2*x1*x1 + .25*e twoway (scatter y x1) twoway (scatter y x2) reg y x1 Source | SS df MS Number of obs = 100 -------------+------------------------------ F( 1, 98) = 8.84 Model | 5.47361726 1 5.47361726 Prob > F = 0.0037 Residual | 60.7044549 98 .619433213 R-squared = 0.0827 -------------+------------------------------ Adj R-squared = 0.0734 Total | 66.1780722 99 .668465375 Root MSE = .78704 ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1 | .2351363 .0791006 2.97 0.004 .0781637 .3921088 _cons | -.0891622 .0787041 -1.13 0.260 -.2453479 .0670235 ------------------------------------------------------------------------------ linktest Source | SS df MS Number of obs = 100 -------------+------------------------------ F( 2, 97) = 16.47 Model | 16.77682 2 8.38840998 Prob > F = 0.0000 Residual | 49.4012522 97 .50929126 R-squared = 0.2535 -------------+------------------------------ Adj R-squared = 0.2381 Total | 66.1780722 99 .668465375 Root MSE = .71365 ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- _hat | .0406711 .366758 0.11 0.912 -.687242 .7685843 _hatsq | -5.123111 1.087467 -4.71 0.000 -7.281432 -2.96479 _cons | .2356118 .09129 2.58 0.011 .0544264 .4167973 ------------------------------------------------------------------------------ reg y x1 x2 Source | SS df MS Number of obs = 100 -------------+------------------------------ F( 2, 97) = 211.06 Model | 53.8122412 2 26.9061206 Prob > F = 0.0000 Residual | 12.365831 97 .127482793 R-squared = 0.8131 -------------+------------------------------ Adj R-squared = 0.8093 Total | 66.1780722 99 .668465375 Root MSE = .35705 ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1 | -.2250357 .0429671 -5.24 0.000 -.3103135 -.1397579 x2 | .8366763 .0429671 19.47 0.000 .7513984 .9219541 _cons | -.0891622 .0357047 -2.50 0.014 -.1600262 -.0182982 ------------------------------------------------------------------------------ linktest reg y x2 c.x1##c.x1 Source | SS df MS Number of obs = 100 -------------+------------------------------ F( 3, 96) = 317.49 Model | 49.9156841 3 16.6385614 Prob > F = 0.0000 Residual | 5.03102284 96 .052406488 R-squared = 0.9084 -------------+------------------------------ Adj R-squared = 0.9056 Total | 54.9467069 99 .555017241 Root MSE = .22892 ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x2 | .8084067 .043878 18.42 0.000 .7213097 .8955038 x1 | -.2207158 .0437682 -5.04 0.000 -.3075949 -.1338367 | c.x1#c.x1 | -.229229 .0193762 -11.83 0.000 -.2676904 -.1907676 | _cons | .1377745 .0298669 4.61 0.000 .0784893 .1970598 ------------------------------------------------------------------------------