I would like to investigate effect of a treatment in randomized control trial. Also, I would like to investigate the moderating effect of motivation (of the participants who are included in the treatment group).

I wanted to use a multiple linear regression with an interaction term in this way:

y= alpha + beta_1 * treatment dummy + beta_2* motivation + beta_3* treatment dummy * motivation

Then, I realized that motivation will not be measured for the participants who are only in the control group.

Would it be possible to use the following model instead?

y= alpha + beta_1 * treatment dummy + beta_2* treatment dummy * motivation (setting motivation zero for the control group)

Cheers,

floriisco