Why R is not significant (and very low), while all predictors are significant? [duplicate]

I used a network logistic regression to regress five predictors against a dependent. They are all significant, instead the R is not significant and it's even very low. I can understand that it may be low because I need to add predictors but I cannot explain why it's not significant. Do you have any idea about?

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Short answer: please check what R^2 value you are reporting. Many LR implementations report pseudo R^2 values such as McFadden or adjusted McFadden for which values in the range 0.2-0.4 indicate good model fit. See this guide on psuedo R and this SO answer

Update:

The individual coefficients can be significant due to the occurrence of significant interactions between your independent variables. For instance, whilst bid price may have an insignificant association to same_cartel alone, the combination of bid price and other variable may generate some significant association to your target same_cartel variable.

It may be useful to assess the collinaearity of your predictors using spearman rank correlation or OLS regression (on any continuous variables) and chi-square (on any categorical variables). Alternatively or in addition, try running your logistic regression with each predictor individually. You could also try step wise pruning if your input variables - though this is not best practice.

If you discover some collinearity between your predictors it is possible to generate a new features by combining the associated variables into a new “interaction term”. This page provides a nice summary of interaction terms.

Also, the model p-values you obtain will depend upon your sample size. If you have a small sample it is more appropriate to comment on the effect and significance of each predictor variable rather than the model as a whole.

• Many thanks BenP. So, I'm working on data on procurement to detect collusion. I'm using the program Ucinet for social network analysis that allow to predict one relationship knowing another one. My dependent variable is "same cartel", that account for whether each pair of companies in my dataset belong to the same cartel (I have 8 cartels). The indipendent variables account the extent to which companies frequently bid together, offer the same price, etc. With 5 predictors I have a too low R-squared (0.026) and not significant (0.858). But all predictors are significant at 0.001. Why? – Mark Apr 3 at 16:09
• Thanks, I updated the my answer. Please could you add the detail to your question also. – BenP Apr 3 at 22:46
• Thanks Ben. I already tried: a) correlations between predictors: they are very poorly correlated - do you think it makes sense in any case to tryinteractions?; b) logistic regression with each predictor individually and they are always significant and in the expected direction. and, as said, in the overall model, all predictors are significant but the model not. what could be the cause? My dataset consists of 1242x1242 observations (it's expressed in this way because it's a matrix, as i said, I'm regressing matrices) – Mark Apr 6 at 5:26
• Ok I’m a little confused now as you said you had 5 independent variables prior. This questsion has now been flagged as duplicate, but I think you should re submit a new question and more clearly describe (with a simplified example) your independent and dependant variables. – BenP Apr 7 at 13:06