Pat -

You can change what is called 'significant' by changing the sample size. As far as the relative importance of independent variables, they really do influence one another, perhaps most notably through collinearity. (Some like to use principal components.)  However, with ordinal data, your information is not so exact. 

I lack experience with ordinal data, but perhaps you might still be able to use subject matter knowledge to decide what variables may together best predict the y-values, and perhaps compare competing models on the same sample by using a "graphical residual analysis." You can search on this term. Graphical residual analyses use scatterplots. You can compare the competing models for another sample on another scatterplot, as you do not want to overspecify for a given sample. See "cross-validation."

For best predictions, you do not want too many variables, or too few, but the best combination.

You might also be interested in the example shown in the appendix in the following open access version of a paper by Galit Shmueli:

https://www.researchgate.net/publication/48178170_To_Explain_or_to_Predict

But you have to apply this to your situation.  I hope this might give you some ideas. 

Cheers - Jim

It looks as though the same question (more or less) was asked here:

https://www.researchgate.net/post/Correlation_and_multiple_regression

Bruce Weaver , this seems to be happening more recently. Do you think it is students trying to get a quick answer for an assignment? It often seems questions like this, which would be covered in undergraduate textbooks.

That could be, Daniel Wright. Or perhaps younger folks struggle with the concept of asynchronous online discussions, and expect this to be like texting or instant messaging. ;-)