If the college or university is close by your home, your student may decide to stay at home while attending school. However, many students are not very happy staying at home with the same rules as they had when they were in high school. Remember, they are adults, even if they may not be ready to live on their own and you will need to be a bit more lenient on such things as curfew and other such things as they are testing the waters and making new friends.
In some cases, it is cheaper for the student to live at home; however, not always. The cost of food at the college, as well, as the cost of maintaining a vehicle including the cost of gas, may make it cheaper for your student to live a bit closer to the college than to live at home.
Many times, students will live at home during their first year of college and then decide if they want to live in a dorm or even share other accommodations off campus with friends they have made.
Of course, this decision is something that needs to be made with you and your student. Either way, if the school is close enough, your student will more than likely come home at least on weekends so you can do their laundry. This may not sound fun, but at least you can see your college student when they run out of clean clothing.
If they do stay at home, it may save you quite a bit of money unless the drive to school is over an hour away which then it may be cheaper to look at other student housing options. Staying at home may give them the opportunity to adjust better to college life at least during their first year before they decide it is time to move out on their own.