You should consider that your data is too noisy to interpret the sign of the correlation with acceptable confidence. The data is not sufficiently conclusive to distinguish a posivite from a negative correlation.
Apart from mere noise, another possible reason for failing to reject a tested hypothesis is to have co-linear predictors in the model. If a set of predictors share the same information about the response, a model is not able to decide which one to "make responsible" for the change in the response - what results in large standard errors. You can check this by having a look at the variance inflation factors (VIFs).
I am not quite sure what you are doing, but if you asked for correlations between variables and with a sample size of 195, I doubt your assumption you have 'strong correlations'. How big are your correlations? Did you calculate a correlation matrix? How many variables?
It is difficult to answer the qustion if you do not provide any furhter details. First - have you run the significance test of correlation and got p-value>0.05 OR have you computed correlation, run a regression and got p-value of the regressors >0.05?
If the first is true, than you simply got correlations insignificantly different from 0, which suggest no linear relationships between your variables. But what are the variables? What are their magnitudes? Sometimes it is advisable to take into account logarithms instead of the original values. If this is not possible, then some people simply get rid of outliers. Or else you can check non-linear correlations. Another question: what is the nature of your data?Are they cross-sectional one or time-series? If the latter - have you checked the stationarity?
However, if the second is true, i.e. you first computed correlations, then run a model, then Jochen Wilhelm already shed some light on the issue.
The answer depends on the type of variables you are using (categorical or continuous) and the analysis you want to run (regression analysis, factor analysis,... ).
Some variables can have nonsignificant correlation.
You want to find the variables influencing the poverty (poor vs nonpoor) or expenditures? The sample unit is family or an individual?
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