I have data on patients before and after an intervention, half have the treatment, half did not. A paired t-test seems a simple way to determine if there is a significant difference after treatment in either group. However there are other variables that I'd like to adjust for, such as age. Could I use linear regression, with the final measurement as the dependent variable, and the initial measurement, treatment group, and age as independent variables, and then see if the 'group' dummy variable is significant?
I see in some papers that ANCOVA is used for this application, but it seems to be mathematically identical to multiple regression. Is there any point to using it?
Lastly, one outcome variable is continuous, another is a scale from 1-10. Is linear regression appropriate for ordered categorical data like this, or is there a method that covers the gap between logistic and linear regression that lets me add in possible confounding variables (such as age)?
Thanks in advance!