Regression not significant on univariate but significant when adding controls I have a data on job type (i.e. dummy variable 1 if bad job and 0 if good job) and amount of debt individuals hold before finding a job. I ran a regression of job type on debt level, and I did not get significance (i.e. p-value was around 0.5). However, when I added the controls (i.e. major while in school, IQ score, etc), I got very significant result on the amount of debt (i.e. p-value less than 0.05). I expected the opposite (i.e. univariate case should be more significant than when I add more controls). Does it mean that I am doing something wrong in the multivariate regression? Or can I say that the amount of debt becomes significant after controlling additional Xs variables? I would really appreciate if anyone can give me advice on this..! Thank you very much!

What you're describing sounds plausible to me (without having much context about the data / problem).
When you're not controlling for anything, debt comes out as insignificant because there's too much noise. For example, you have people who have different levels of IQ, education, family wealth, etc. Sadly, being $50,000 in debt might not have the same consequences for a rich white man who was born in a posh neighbourhood vs. someone from a minority group who was born in a less fancy area.
When you control for these other relevant variables, the model finds it easier to isolate the signal "debt $\rightarrow$ good job".
