Hi,

I am running a regression with indices. Dependent variable is overall index while independent variables are three separate indices. Indices are constructed using scaled (min-max scaling) variables. How can I interpret the coefficients?




Linear regression Number of obs = 35
F(3, 31) = 141.83
Prob > F = 0.0000
R-squared = 0.9170
Root MSE = .04167

--------------------------------------------------------------------------------
| Robust
overall_index | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------------+----------------------------------------------------------------
index_inter | .5919523 .0358884 16.49 0.000 .5187574 .6651472
state _index | .2642096 .0325353 8.12 0.000 .1978534 .3305659
index_val | .0919699 .0554995 1.66 0.108 -.021222 .2051619
_cons | .0179432 .0271987 0.66 0.514 -.0375289 .0734153
--------------------------------------------------------------------------------

Similarly, if I am running the regression with dependent variable being an index while independent variables being scaled variables then how do I do interpretation. An example has been posted below:
Independent variables are min-max scaled while dependent variable is constructed using scaled independent variables. How can I interpret these? As a side note, if I want to assess the contribution of independent indicators/variables towards final index value then is it the right statistical tool to go for? or there can be an alternative to this

Linear regression Number of obs = 35
F(3, 16) = 42.59
Prob > F = 0.0000
R-squared = 0.8308
Root MSE = .07131

------------------------------------------------------------------------------
| Robust
index_health | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
nmr | .228956 .1801838 1.27 0.222 -.1530166 .6109286
umr | .2888295 .1722586 1.68 0.113 -.0763424 .6540014
srb | .197668 .0436583 4.53 0.000 .1051166 .2902195
_cons | .1650322 .0400046 4.13 0.001 .0802263 .2498382


Any advice in this context will be really helpful.