A 15% resistance modifier means what usually deals 100 damage now deals 85 damage.

If you have Vehicle Shield Upgrades at a certain level, then resistance modifiers reduce damage by a percentage of the reduced damage due to the skill's passive resistance bonus.

ie. If your VSU skill is at level 3, you take 94% damage. So applying the 15% resistance modifier then would result in taking 94*(1-.15), around 80%, damage.

Hopefully that's right.

Yea that's how you calculate resistance your resistance.

And to the OP there isn't a module that increase your shields by a percentage. It's a set amount for each module. Rechargers increase your rate by a percentage, but not extenders,

Specifically the local power plant manager increases your shield amount by 7% but that shield bonus of 7% only applies to the vehicles base shield (and not any shield gotten from extenders). I am curious if by the same mechanic a resistance amplifier would only grant its resistance bonuses to the base shield amount.

It seems like it would be an unintuitive/strange way for it to function but that doesn't mean it isn't so.

Effective_HP = (Base) / (1-Total_Resistance_In_Decimal_Form)

Stacking penalties are as follows:

1. @ 100%
2. @ 87%
3. @ 57%
4. @ 28%
5. @ 10.5%
6. @ 3%

Only modules that explicitly say they suffer stacking penalties from similar modules will suffer a stacking penalty.
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For example, if you have 5800 shields, and two 15% ward shield modules:

Total resistance is 15(1)+15(0.87)=28.05
EHP=5800/(1-0.2805)=8061 shields

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Also, for the record, there are modules that add percentage to shields, Local Power Diagnostic Systems for example add +7% to both PG and Shields.

It doesn't work like that because resistance isn't a modifier that is applied to your vehicle at all but is instead applied to the enemy weapon. Just think about taking each unit of damage from the enemy weapon independently. The '1' damage coming in is reduced by your resistance amount and then applied to the shields until your shields are depleted. Doesn't matter if the shields are the base amount or if they are from a module the damage will be reduced the same.

The only quirk about resistances is that the stacking penalty affects them a good deal more than it does something like damage modifiers and when using resistance mods of different values the penalty will be applied to them in an order that will give the least resistance which is the opposite of how it works for everything else.

EDIT: Forgot about the pg module that also grants shields. The reason that only applies to the base is because modules that grant set amounts aren't modified by anything else and are always applied last. It just has to do with the order the calculations are performed, the game doesn't differentiate between base shields and shields from an extender.

I do have another question though. What do you mean the stacking penalty affects resistance mods more than others. Is it just the order the penalty is applied as you say or are the %'s different? I haven't heard anything about that.