if someone else gets a speeding ticket in my vehicle, does it increase my insurance?

If someone else is driving your car and receives a ticket, the ticket will be charged against the driver, not the owner of the car.  You have no liability for this type of incident.

If there is an accident in your car,  caused by someone else, the insurance on your car will pay for the damages or injuries caused in the accident.  However, your insurance rates will not go up since you were not the driver, presuming that person is not listed as a driver on your policy.

If the person who causes the accident is a member of your household, and not listed as a driver, your insurance company will want to add them to your policy, unless they have their own car and driver.  If they do not, then they will be added to your policy and the rates will go up since the driver will then be listed on your policy.   If you do not want that to happen, then you would have to exclude the driver from your policy and not let them drive your car anymore.