I was asked a question recently which I could not find an answer for and was hoping someone could enlighten me.

The question was regarding the significance of a single variable in a linear model.

What is the difference between a traditional p-value {which you would obtain from the t-statistic formula (b1 - b0) / se(b1)} and log-likelihood ratio between a model with the variable in question, and a model without.

In the log-likelihood case, would a significant LLR suggest that the variable had a significant impact on the model? Assuming the LL for the full model was better than the subset model.

Is this result comparable to a traditional t-distribution p-value one would normally get from a linear regression? If not, why not?

Thanks in advance, and please ask for any additional details if I was not clear.