I am helping someone with a project and want to be sure I am understanding how to interpret this correctly. We are running a simple OLS regression where we are predicting a continuous DV (number of jobs applied to) and our two main IVs are race (black versus not black) and occupation (white collar versus blue collar). When we run the regression with a host of controls, the results show that none of the main coefficients are significant:
Blue_Collar (.9, p=.7) BlackXBlue_Collar (-6, p=.19)
For the predictive margins, only two of the four categories are significant. Black/Blue Collar and Non-Black/Blue Collar are significant and the margins plot shows a significant difference between these same two categories: there is a significant difference between Blacks and Non-Blacks in blue collar where blacks apply to fewer jobs than non-blacks; but there is no difference between the two groups in white collar jobs.
Though I have a basic level of statistical knowledge I am not sure what to make of these results, specifically: 1) How does one make sense of these predictive margins and plots when the coefficients in the underlying model are not significant? I would have expected a negative and significant coefficient on BlackXBlue_Collar to correspond with the predictive margins. What trumps in this case, the coefficients or the plot?
2) For the predictive margins is the null that each of these values = 0? In other words, does significance here mean that the predictive margin differs from 0? Or are these being compared to each other?