# Help me interpret this negative linear regression [closed]

This is the output I have for a multiple linear regression I did in R.

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)                            1.936e+01  8.196e-01  23.627  < 2e-16 ***
dados3$$income -1.278e-03 5.784e-04 -2.209 0.02721 * dados3$$indice_gini                    -1.430e+01  1.247e+00 -11.470  < 2e-16 ***
dados3$$month_wage -1.775e-01 9.515e-02 -1.866 0.06212 . dados3$$perc_extreme_poor_kids          3.854e-02  1.216e-02   3.169  0.00154 **
dados3$$perc_poor_kids 2.159e-01 1.148e-02 18.812 < 2e-16 *** dados3$$perc_pop_with_prop_Wc           5.055e-02  6.021e-03   8.397  < 2e-16 ***
dados3$$perc_pop_w_houses 4.297e-02 7.924e-03 5.423 6.12e-08 *** dados3$$perc_pop_with_trash_disposal   -7.045e-03  6.520e-03  -1.080  0.27999
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.038 on 5555 degrees of freedom
Multiple R-squared:  0.6804,    Adjusted R-squared:  0.6799
F-statistic:  1478 on 8 and 5555 DF,  p-value: < 2.2e-16


In my interpretation, the equation yielded a negative regression. Where as one independent variable decreases, it increases the dependent variable (in this case child mortality rates). An interesting observation I noticed was that the gini coef decreases, and meanwhile the child mortality increases (the contrary was supposed to happen). Is my interpretation correct?

• Your interpretation is correct, but you almost certainly have collinearity which can do weird things to parameter estimates. Have you checked for collinearity? – Peter Flom - Reinstate Monica Nov 8 '19 at 14:37

## 1 Answer

Your interpretation is correct, but in your model, you also control for typical income and wage, so the interpretation for the Gini effect gets tricky if you are holding those fixed. It is hard (though maybe not impossible) to conceptualize how you could get a more unequal distribution of income without a change in average income or wages. One possibility is that the rich and poor get more at the expense of the middle. If child mortality is concentrated at the bottom of the income distribution, this shift of income there should help lower mortality by a lot. Moreover, if child mortality reductions are enabled by progressive taxation (maybe through additional hospital or other public goods funding), it is possible that this could also help. To sum up, regression coefficients require the "all else equal" clause for correct interpretation. There is another nice example of that here.

I should also point out that, in addition to issues of interpretation, regressions usually don't give you casual effects, only biased versions of them. Sometimes the bias is big enough to flip the sign of the effect. Your intuitions about causality may not match the regression output for that reason as well. Simpson's paradox is one example of this.

• Thank you for the heads up Dimitriy, really productive comment! I know it's out of the scope of this model, but something you said made me curious, "regressions usually don't give you casual effects, only biased versions of them". In this case which kind of analysis would you recommend? – Omar Charming Khodr Nov 8 '19 at 1:01
• Experiments are one option, though not always feasible. There are "causal inference" techniques that can work with observational data under some assumptions. The econometrics tag here is a good place to start learning about them. – Dimitriy V. Masterov Nov 8 '19 at 3:36