Don’t use increase of when you want to say what is increasing. Use increase in:
✗ Is gun ownership connected with the increase of violent crime?
✓ Is gun ownership connected with the increase in violent crime?
✗ The depletion of the ozone layer could cause a serious increase of skin cancer.
✓ The depletion of the ozone layer could cause a serious increase in skin cancer.
Use increase of with a number or percentage when you want to talk about the amount by which something increases:
There has been an increase of nearly 30% in spending on hospitals.