How do you interpret if your Poisson regression intercept has a significant p-value but no other terms have a significant p-value? My model is trying to determine if Big Five personality traits influence how likely people are to follow COVID-19 guidelines. The results seem odd since the intercept has a significant p-value, but the Big Five trait terms do not.
Are these results anomolous? Please explain what they mean in depth.
Table of results
Figure of results
 A: The Poisson regression model is given by
$$\begin{split}Y|\lambda &\sim Poisson(\lambda)\\
\ln(E(Y|\lambda))&=\ln(\lambda)\\&=\beta_0+\beta_1openness+\beta_2neuroticism+\beta_3extraversion\\&\qquad\,\,+\beta_4conscientiousness+\beta_5agreeableness\end{split}$$
You only got that the intercept is significant. Your model reduces to:
$$Y|\lambda\sim Poisson(\lambda)\\
\ln(\lambda)=\beta_0$$
This means that the average number of people who follow Covid-19 guidelines has a constant mean through your data, given by $e^{\beta_0}=e^{8.78}=6502$ and your model reduces to a Poisson model, $Y\sim Poisson(6502)$.
Given that your pvalues are all insignificant, it means that the other variables shouldn't be included in the model. But if they were, let's see how to interpret them. The coefficients are about 1, so for openness, an increase in openness by 1 increment corresponds to an increase in the mean number of people who follow Covid-19 guidelines by 1 on the log scale, or by a factor of $e^1=2.78$. That is, increasing how open people are by 1 increases the average number of people who follow guidelines by a factor of 2.78.
