You can confirm that "probably" with 5 minutes of research and find out that the largest contributors to carbon emissions in eating are the production of the raw materials (which ingredients you use). Once that is controlled for, cooking method is the largest second factor (wood / coal / gas / electric). Once that's controlled for, going out to eat in a restaurant is worse than at home. The only communal eating that is more efficient is school / soviet canteen style eating, which is not what you were thinking about when you said restaurants.
