I am trying to determine if I should include an "intercept" or a "trend and intercept" when using the Augmented Dickey-Fuller (ADF) test. I ran a regression with my dependent variable and a time trend and both the intercept and trend were statistically significant. Is this statistical significance what determines if I should include a "trend and intercept" in the ADF test? My data is unstructured/undated. The series contains 252 observations and there are about 6 observations per year from 1970-2014. Below are my regression results and a graph of the raw data.