My data are proprietary. So, I am altering the data context a bit because I have signed an NDA agreement on the original dataset. This made up context, which mimicks my actual dataset, is about runners i.e., athletes. In my data situation, each athlete can either: (1) run indoors on a treadmill - I call this "DIST_INDOORS_1" (2) run indoors on track in the gym - I call this "DIST_INDOORS_2" (3) run outdoors on track in the ground - I call this "DIST_OUTDOORS".
The sum of "DIST_INDOORS_1, "DIST_INDOORS_2, and DIST_OUTDOORS is my dependent variable. I call this dependent variable, "TOTAL_DIST".
Data were collected over a single day, but over a large number of athletes. As indicated earlier, my dependent variable is TOTAL_DIST, but one of my important independent variables is DIST_OUTDOORS". However, I am NOT going to use DIST_INDOORS_1 are DIST_INDOORS_2 as independent variables. on and/or outdoors. Again, I will only be using DIST_OUTDOORS as the independent variable in the regression of TOT_DIST. I have several other independent variables, such as age, gender, height, number of years of prior training etc.
My question is as follows: Can I run a linear or a count model (such as Poisson or NegBin regression) of TOT_DIST using DIST_OUTDOORS as one of the independent variables? I will be including other independent variables, but will NOT be including DIST_INDOORS_1 and DIST_INDOORS_2 as independent variables. Or, will I need to execute some fancy regression? If so, which one? Advice/inputs will be greatly appreciated. Thanks in advance.