First I want to thank the devs for adding more detailed, clear information to the stats screen. It is now obvious that when it comes to damage and armor, the elemental and non-elemental are components of a figure that can be summed. It is also indicated that the mod stats are multipliers.
Additional experiments (thank you, bodaciouschampion8/thewholebutthole!) have revealed an odd situation that will make it very difficult to learn anything further about the attack stats using the method of adding gears. There is an apparent granularity to the amount of damage added by a quantity of attack. In other words, damage is added in increments of 2 (no element advantage) instead of 1, and because it requires more than 2 attack to get this 2 damage, there is some minimum amount you need to add to see any difference. This amount is difficult to pin down, but it is at least 18 for the characters I tested (cinder and caine).
This messes up the experiments because adding 2 gears will not always add even 1 damage. In fact, the first experiment found that edge by dumb luck; if it hadn’t, I would have come in here saying that elemental attack does nothing! It also interferes with linear regression for the same reason.
It is still possible to conduct experiments on armor/defense stats, as long as there isn’t a similarly insensitive granularity there as well. What we will do is similar, but rather than adding 2 gears that improve an attack stat, it will be a defense stat, and rather than shooting the test target, the tester will shoot the subject and record damage done. In that way we can discover whether defense is deducted from each bullet, decreases the proportion of attack relative to damage, or decreases the effective value of the attack stat. This is one of the more important distinctions because it affects the degree to which rate of fire is important. If every bullet has its damage reduced by the same amount, then fast-firing guns are disproportionately affected by defense, and it will be slightly more difficult to learn anything from the given attack stats. But it will be good to know.