Msybe you can look a Primary Component Analysis.

The most important thing is that you have the relevant and accurate data.

While we running a multiple regression analysis, our interest is not only to identify the significant determinants but also to determine the most important factors which often based on the size of the regression coefficient. In that dimension and since you just want to rank the factors based on the regression weight, I think there is nothing wrong in your procedure. However, as you said consider only the factors significant in regression.

I don't think so. People use Principal Component Analysis for the purpose. But I am not a fan of PCA for the purpose. PCA gives u weights which are dependent on your data set. If you use a different set of data, then your weights, and hence the index, will change. You may consult relevant statistical text for an answer. In some cases perception survey results can be used to decide the weights

It is not clear what specification you take for your estimation and which data you use. I assume your equation will look like

R = a1*X1+a2*X2+….+b1*Y1+b2*Y2+….

with R as gross product, Xi innovative and digital factors and Yj other factors. I do not mention possible transformations of the variables or non-linear functions. The coefficients ai and bi cannot be used as weights (because they are dependent on measurement), unless all variables are in logs (which means that coefficients are elasticities) or have the same dimension (which is rather unlikely). Another possibility may be that you first regress R with the Y’s and then the residual with the X’s, which would enable to use different functional forms. Whatever your choice, you should always look at the one-by-one relations of the variables (diagrams, correlations) before econometric estimation.

Needless to say, that there may be numerous problems connected (theory, multicollinearity, transformations, unrealistic results etc.) with your project and it would likely mean to input much work for a poor result.

I do not like rankings: For me “rankitis” and “indicatoritis” are severe epidemics not only in economics, but in other “sciences”, too.

Dear José-Ignacio Antón and Madhurjya Prashad Bezbaruah thank you for your comments.) I will look into PCA for more details. Anton Rainer , thank you for your opinion.) I do agree, that rankings is a curse, however politicians like them a lot and it is hard to change their way of thinking. This project comes more from politician side and the best, what we can do, is to construct this rating in a more scientific manner. I hope that this will result in something usefull and more suitable for analytical purposes. Saji T.G , thank you for sharing your opinion.)

Maybe you can use DEA (Data envelopment analysis).